Isn't it interesting how "people of color" is a common self-designation for (most frequently) black people, whereas "colored people", literally synonymous, is considered offensive? Of course there are valid historical reasons for it, but many people (probably including GP) don't know about them.
Well, the GP uses "our" in reference US history, and I've never met a single American under the age of 40 who doesn't know that most people consider "colored person" offensive, even if they thought it was a stupid reason.
Like most things considered racially offensive, it's less about the dictionary definition of the word and more about what the connotation is. It's the same reason someone in an interracial marriage would hardly ever say "my black wife" but would say "my wife, who happens to be black," if it were relevant. I'm 100% positive they'd never say "my colored wife" unless they were 130 years old.
"People of Color" means "non-whites", so includes pretty much everyone but Europeans. It's used instead of "non-whites" to describe a demographic by an attribute they have, instead of an attribute a different group has.
Calling them "colored people" certainly doesn't help.