Why are people of color so against being called colored people? It means the exact same thing.

No, it doesn't. There is a lot of history behind slang terms used to identify people of color. And the terms aren't limited to "black" people. Lots of confusion and tension is being created by people insisting on using labels to identify one's self and others. What may seem like an innocent term may actually be used for derogatory purposes later. Some terms may only be used by certain people. And terms we grew up with are not acceptable now. I would try to educate yourself on the topic in general.