I really don't think it's crazy that I want my brother to do the dishes
Why do you think your brother should do the dishes?
Because he eats a lot of food at home.
That makes sense, people should clean up after themselves. Household chores should be shared by everyone, and it is expected that people will all help, especially when they create a mess.
I'm going to get him back all the time by fucking his life up.
I think a better approach in getting him to help with dishes is to sit down as a family and have a conversation about responsibilities. Once expectations are set he may willingly start to pitch in more. Then you don't have to worry about building up resentments.