Readers are never told exactly why Brian's parents got a divorce, but we are told that the divorce proceedings were initiated by Brian's mother. Throughout the first half of the book, Brian keeps remembering the divorce and "the Secret." It's a secret that his mother kept from his father; however, Brian knows what the secret is. Brian's mother is having an affair with another man, and Brian knows it.
In the mall. Every detail. His mother sitting in the station wagon with the man. And she had leaned across and kissed him, kissed the man with the short blond hair, and it was not a friendly peck, but a kiss. A kiss where she turned her head over at an angle and put her mouth against the mouth of the blond man who was not his father and kissed, mouth to mouth, and then brought her hand up to touch his cheek, his forehead, while they were kissing. And Brian saw it.
Saw this thing that his mother did with the blond man. Saw the kiss that became the Secret that his father still did not know about, know all about.
It's possible that there was other stuff going on between Brian's parents that Brian doesn't know about, but the text makes it fairly clear that Brian believes that his mother wanted nothing to do with his father anymore because of this other man. To make matters worse, she never tells her husband about the affair or why she wants a divorce. She just wants the marriage ended. Brian knows the reason and feels it is his responsibility to tell his father.
The burning eyes did not come back, but memories did, came flooding in. The words. Always the words.
The big split. Brian's father did not understand as Brian did, knew only that Brian's mother wanted to break the marriage apart.