Why did Kevin say that he didn't mean it and that he'll never be a pain again when he looked at his family's picture?

Because he over-reacted to Buzz eating the cheese pizza. Also, he "wished" his family gone and they did go away. Given that he believed he was responsible for his family disappearing, his guilt would mean he would be willing to accept he was more at fault for the incident that he otherwise would have.

8-year-olds aren't exactly always the most reasonable or logical. He was being treated like a pain in the butt... so he probably assumed he was being a pain in the butt.

Apologizing for his perception of what he thought he did wrong was a last ditch effort to get out of the situation he found himself in.

It was his and Buzz's fault. And the parents' fault for being ignorant of what a bully Buzz was. I can relate to Kevin since when I was a kid I'd only want to eat pepperoni pizza.