Many of Max's dislikes in Freak the Mighty can be linked to his severe low self-esteem issues.
From the beginning chapters, we know that Max doesn't like himself for a couple of reasons. He refers to himself as a "butthead," "brainless," and "dumb." This could be due to the fact that he has been labeled as learning disabled and gets treated differently at school. We also know that he doesn't particularly like school and allows Kevin to answer all of the questions. This is even after the teacher probes Max to answer - he answers by putting his head down and letting Freak continue.
Max is also very self-conscious of his appearance. He is very large for his age and shows no signs of stopping anytime soon. His appearance really bothers him for the fact that he looks exactly like his father. This makes his grandparents particularly uncomfortable, since his father - which we learn later in the novel - actually killed Max's mom. We really learn how much Max looks like his dad when he ends up actually startling Freak's mom when they first moved to the neighborhood.
Max's friendship with Freak, however, helps him overcome these issues when Freak gifts him with the journal so that he can write all of his adventures down. Furthermore, Freak helps him feel closure regarding his past with his dad.