There are several conflicts for Chris Keller that stand in the way of an open relationship with Ann. First, Ann was his brother, Larry's girl, she was always going to marry Larry, it was just the way it was. This is illustrated by Kate Keller, who refuses to think of Ann as being an individual who should be allowed to move beyond her attachment to Larry. Kate would rather memorialize Ann's life by referring to her as "Larry's Girl."
Kate Keller is fiercely opposed to Ann and Chris getting together or getting married. She resists accepting the possibility of Ann and Chris together, because if they get together, it means Larry is really dead.
The other conflict that plays a major role in Chris being unable to love Ann openly is the revelation that his father framed her father for the faulty airplane parts being shipped to the military. Steve Deever is currently serving prison time, while Joe Keller is free based on the lie he told to the court.
Once Ann discovers that Steve has been languishing in jail, ignored by his family, rejected by his daughter for something that he had no control over, following Joe Keller's orders, she could never love or marry Chris Keller.
Chris, when he finds out that his father was responsible for the death of several pilots, and his brother's suicide, as a principled person, he is emotionally crushed, completely numbed and disgusted by the idea.