How does Troy view fatherhood in Fences?
Troy feels that his role as a father is to provide his son with discipline and opportunity. Troy insists that Cory refrain from playing football and he expresses his reasons. Football will not provide Cory with the skills to succeed that an education and work experience will provide.
Cory accuses his father of being competitive, but Troy claims to be helping Cory to avoid the same disappointments that he faced himself in his baseball career. The attitude of control and the inability to express his feelings softly seem to be traits continued from Troy's own childhood.
His father was brutal and controlling, and although Troy loves Cory, he knows of no other way to bring up a son.
Troy's parenting shows no yielding. He cannot even tell his son that he likes him when Cory asks this rather vulnerable question. As Cory grows more rebellious and assertive, Troy becomes increasingly combative and stern. Troy's inability to allow Cory to pursue his interests and to express any self-will work to sever their relationship.
Unable to compromise, to soften his position, Troy pushes his son away (violently) and never gets him back.
The audience should reasonably suspect that Troy is denying his true motivations regarding his parenting decisions in the same way that he denies his own responsibility for his failure in baseball and in marriage.