When Cory expresses a desire to play football and use the sport to help him go to college, Troy refuses to allow Cory to quit his job at the A&P.
Troy intuits right away that Cory's story about working on the weekends during the football season is a lie. Cory tells Troy that he has been promised his job back when the season is over and that he will be able to work weekends at the A&P while playing football.
When Troy goes down to the A&P and finds that he was right and that Cory no longer works at the A&P, he then goes to the school and pulls Cory from the football team.
Cory sees this as an act of jealousy, saying that Troy is worried that Cory will be a better athlete than Troy ever was. Troy claims otherwise.
Troy wants his son to achieve a future that does not include hauling garbage.
Cory cannot accept Troy's claims, at least in part, because Troy never communicates his love for his son. Rose tells Troy that Cory simply wants to hear him say, "Good job, son." Yet, Troy takes a hard line with Cory and refuses to deviate from it. This is a result of Troy's own family history.
His father was brutal and controlling, and although Troy loves Cory, he knows of no other way to bring up a son.