Why does David get so angry when Larry Jr. was picking on him and Chris in The Lost Boy?

You can find the answer to your question in chapter 5.
In that chapter, we learn that Larry Junior always picked on David and Chris whenever he liked. During one especially trying episode, David became enraged at Larry Junior's behavior. This is because Larry Junior used his size against the younger boys. In other words, Larry Junior bullied David and Chris simply because he was bigger and stronger. He knew that neither David nor Chris had the wherewithal to defend themselves against him.
Additionally, Larry Junior always ridiculed Chris's disability when he terrorized the younger boy. The latter suffered from cerebral palsy and stuttered every time he spoke. As for David, he was short for his age, and Larry Junior never ceased pointing out the fact.
All in all, David became enraged because he was tired of Larry Junior using his size to bully boys who were weaker and younger than him. David was especially upset at Larry Junior for ridiculing Chris's disability. After all, Chris had little power to change his physical and mental condition. He was helpless, which made Larry Junior's behavior even more repulsive.