Troy's strict approach is due to the fact that he doesn't want his son to repeat his own mistakes and suffer his own disappointments.
When Troy was young, it looked like he was to have a promising career as a baseball player. However, he was never allowed to play in the Major Leagues due to the color of his skin. He is worried that, in a similar way, Cory's prospects on the football field may be limited because he is black.
However, he takes this concern far too far and becomes mean in his attempts to get Cory to follow what he would consider to be a more practical career path. He is an extremely blunt man, and he does not reassure Cory when Cory asks him why he has never liked him. He instructs Cory to go and get back the job that he had previously and refuses to sign the college football recruiter's form.
Cory defies him and does not go to the A&P to get his job back. His father's response is to go to the football coach and ensure that Cory isn't allowed to play at all anymore. While this response is undoubtedly mean, it is simply Cory's response to the upset and disappointment he suffered earlier in life when his baseball career failed to launch.