Troy and Cory Maxson. Troy harbors an undying but quite bitter (and failed) dream of becoming a professional baseball player. He was a good player, but too old for the major leagues by the time he got out of prison. Troy refuses to admit he was too old, however, and prefers to blame race politics (e.g. racism) for his failure to make the Big Leagues. 

While there is a grain of truth to Troy's complaint and ample reason for him to point out the racist policies that might hamper him elsewhere in his professional and social life, Troy's dream of sports success was ruined by his own faults and flaws -- by his life as a criminal. 

In this way, Troy's relationship to sports is somewhat complicated and less than pure/innocent. It is tainted. Cory's ambitions with sports are equally complicated but not at all tainted. Cory wants to use sports to get a scholarship and go to college. Thus, Cory brings his own motives to his relation to sports. 

Due to the complexity of Troy's views of sports, we can only ask if Troy demands that Cory quit the football team as a means to protect his son from disappointment and hurt; from becoming a subject of racism. And we can only ask if he is instead engaging in a competition with his son, setting a limit on Cory so that Cory will not surpass his own achievements. Either of these possibilities is possible. 

In any event, Troy refuses to understand Cory's very specific ambition to get into college on a scholarship and so, by default, sets a hard limit on the possibilities of Cory's life. When Cory enlists, he is choosing perhaps the only option left open to him to maintain an expansive view of the life ahead of him. This trajectory is a crucial difference between Cory and Troy as Troy notably spends his time railing against the limits (fences) that have hampered and hindered him from becoming what he might have been in his life.

Cory still has a chance to hit a home-run, as it were, with his life. 

To encapsulate the relationship between Cory and Troy, we might describe the dynamic between them as competitive and rooted in history. 

Each character sees this conflict differently. For Cory, Troy is creating a rivalry with him regarding sports. 

Cory feels that Troy is refusing to allow him to play football out of a jealous impulse. He thinks that Troy is worried that he will become a better athlete than his father. Cory also feels that Troy simply does not like him. 

Troy, with a quite different take on the situation, feels that he is attending to Cory's best interests by pulling him from the football team and refusing to sign the recruitment papers.

Troy is unable to accept that his son might succeed where he had failed—and Cory accuses his father of just such a motivation. But it is more than a desire to control Cory's success that is at the heart of Troy's actions.

Troy continues to harbor an abiding bitterness regarding his athletic career. He wants to keep Cory from experiencing the same bitterness. He also wants to make sure that Cory does not end up hauling garbage for a living. Troy wants Cory to have a better life than he has had. 

The conflict between the father and son is part rivalry and part insistent paternal care. However, Troy's failure to communicate any love or kindness to his son leads Cory to see only the rivalry and none of the care. The two become cut off from one another largely as a result of Troy's inability to yield any affection or softness to his son.

Unable to open up to those that he loves, Troy keeps much of his emotion inside, building imaginary fences between himself and his family and friends.

Troy cannot say that he likes or loves his son when Cory directly asks him the question, "Why don't you like me?"

Later, he cannot admit to his failures as a husband and father and, in his stubbornness, he repeats a regrettable episode from his own past, fighting with his son and forcing Cory to leave home.

In August Wilson’s playFences, Troy and Cory have a complex relationship. The main conflict between them is that Troy does not want Cory to pursue football. Cory is offered a football scholarship, but Troy refuses to sign the college recruiter’s form and tells Cory to get his job back at the A&P. During the conversation, Cory brings up a deeper issue: Troy’s lack of affection. He asks him about this:

Cory: How come you ain’t never like me?

Troy: Liked you? Who the hell say I got to like you? What law is there say I got to like you?

The exchange reveals that there have been years of tension and coldness between the two of them. Cory is upset by his father’s stubbornness, and as a stubborn person himself, he does not listen. Troy eventually goes to Cory’s football coach and tells him that Cory can no longer play.

While Troy is extremely tough on his son, it is interesting to consider how his own background impacted who he became as a parent. He left his abusive father when he was fourteen, and his dreams of being a baseball player were impossible because of racist policies. This experience shaped his own perspective on how to relate to a son and made him unable to see that Cory’s experience with football could be different than his experience with baseball.

The tension between the two of them escalates when word gets out that Alberta is going to have Troy’s baby. When Troy is fighting with Rose, Cory intervenes and punches him. Several months later, they have a fight with a baseball bat and Troy tells Cory to leave the house. They never talk again, but Rose talks Cory into going to his father’s funeral out of family loyalty.

The question is correct in identifying the parental relationship as one where there is generational conflict converging with personal difficulty in articulating emotions.  This is the setting in which there is challenge in the relationship between Cory and Troy.  In the end, this is what causes the rift between them.  Troy has seen life at its very worst, experienced what it means to endure the ruptured bonds of both dreams and relationships, and understands the downside offered in a social setting that marginalizes on both race and class conditions.  In contrast, Cory is part of a younger generation that believes in its own promises and possibilities.  He interprets his father's fears and poor articulations of emotions as being stifling and realities imposed on the father from the son in the attempt to cut off the latter's chance at happiness.  There is a generational issue present, but it is also hampered by the presence of social conditions that take away at one's heart and soul, at one's state of being in the world.  The father seeks to protect his son from such a reality, something that the son sees as oppressive and repressive, a reaction that the father sees as ingratitude.

The first conflict between Troy and Cory is in regards to chores. Rose reminds Troy that he has said he would complete the fence in the yard and Troy insists that he will get it done, but Cory needs to put some effort into helping. 

When Cory leaves home on a Saturday morning for football practice without finishing his chores first, Troy is waiting when he gets back home. Troy reprimands Cory for leaving without doing his chores. 

In this conversation, Cory states his interest in playing football and Troy says he will not allow Cory to quit his job at the A&P.

This is the moment Cory asks why Troy doesn't like him. Troy responds that as his father, he does not have to like his son. The only demand he feels in relation to Cory is to raise him properly and to provide for him. 

The confrontation ends with Troy telling Cory to get back down to the supermarket and get his job back.

The themes of the trouble between father and son are established in this scene. Troy refuses to yield to his son in any way, showing no affection, offering no reassurance, and setting down absolute rules of behavior. For his part, Cory expresses his need for some sign of approval from his father and gets nothing of the sort. 

Troy is locked into a mode of parenting learned from his own father.

His father was brutal and controlling, and although Troy loves Cory, he knows of no other way to bring up a son.

As the play goes on, Cory defies Troy's order to quit the football team and get his job back. When Troy finds this out, he confronts his son and tells Cory that this defiance is the first strike. He warns his son not to take more steps in this direction. 

Strike two comes when Troy and Rose have an argument and Cory steps in to protect his mother, knocking Troy to the ground. Troy refrains from retaliating physically, but warns Cory again, warning him that this is his second strike and telling him not to strike out.

This episode is similar to one that Troy relates about his own childhood. When Troy was fourteen years old, he fought with his father over a young woman. That episode caused a permanent break between Troy and his father, launching Troy into the world to fend for himself. When Cory accosts his father, we see the potential for a similar break between these two men. 

When Troy is at his lowest point, having lost his mistress, Alberta, when she dies during childbirth, and losing his wife's respect and affection at the same time, the conflict between Cory and Troy comes to its climax. 

Cory comes home and tries to step around his father to get into the house. Troy refuses to move and the two scuffle and fight. Troy's refusal to move can be read symbolically, as he has continued to alter his behavior over the course of the play. 

The nature of the conflict between Cory and his father can be seen as stemming from Troy's inability to change, to move, or to depart from the mode of behavior set by his own father (a man who Troy himself dislikes intensely).

By the end of the play, Cory has realized that Troy will never yield or change. Cory no longer hopes for approval from his father. When Cory tries to physically move his father, the final break is made between father and son. 

In the end, Cory leaves the house for good, and Troy ends the scene with a taunt for death to come.

The father-son conflict between Troy and Cory forms the dramatic heart of the play. Much of that conflict is generated by Troy, reliving the fraught relationship he had with his own father. Troy has a sense of duty towards Cory, as with the rest of his family, but that's about the only bond he has towards his son. Troy doesn't like Cory and says so frankly, but so long as he's working hard and putting food on the table he thinks that's enough to make him a good father.

And it's in their respective attitudes toward work that the conflict between father and son finds its most notable expression. Having been denied the opportunity to develop his skills as a baseball player in his youth, Troy doesn't see why Cory should be allowed to avail himself of similar opportunities in football. Troy has had to work for everything he's ever had, and as far as he's concerned, Cory should too. Hard work is one of the few things in life that gives Troy a sense of worth and dignity in such a deeply racist society.

Yet Cory, in playing football and later joining the Army, shows a greater willingness to compromise with white society and its values. By ordering Cory to quit the football team, Troy probably thinks he's protecting him from the kind of prejudice and disappointment that he experienced back in his youth. But at the same time, there's a sense of resentment here, that Troy finds it unfair that his son should be able to make a success out there in the big wide world in a way that he was never able to.

Troy and Cory are so much alike, and ironically this proves a real sticking point in their relationship. Both are very proud, stubborn, set in their ways, and unable and unwilling to back down in an argument. Yet there is one crucial difference. Over time, Cory develops a self-confident personality, a personality free from the kind of hang-ups and burning resentments that dogged Troy for the whole of his adult life. This allows him to be the bigger man, to reconcile himself with his father by showing up at his funeral. But it says a lot about this tense relationship that this reconciliation can only occur in death, not life.

Most of the conflict between Troy and Cory is seen in Scene Three.  It is here where Troy questions Cory about the pursuit of his dream of playing football.  Practices and time committed to the sport has caused Cory to quit his job at the supermarket and neglect chores.  Troy is opposed to Cory's pursuit on two levels.  The first is that it reflects the power dynamic between father and son, with the latter doing something that the former does not embrace or endorse.  The second level is something that Rose brings out in the next scene that Troy might be displacing the frustration and sadness at the denial of his own dream of playing baseball, something that never came to fruition and haunts him because of it.  The conflict is not necessarily resolved at the end of Scene 3, but it is shown to be one where the father demands complete control of the father's life and the son having to wrestle with the fact of following this control or going against it.