"People help other people because it makes them feel good". I'd say the meaning is "people help others in need so they can feel good". Is there a problem with this? If someone in need of help receive that help, they will feel alleviated, while people giving help will feel good. I don't know, it sounds great to me. Even if the helping ones wouldn't feel a thing, like robots, it would be still great, in my book, because someone in need is being attended.

Now, if the helping ones feel bad for helping, and the others feel good, then I can see an issue. The only problem I could see is to be angry because there are people in need to start with.