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.