How would you feel if I called you an idiot? Probably not super thrilled. What about if I called a person with severe cognitive disabilities an idiot? A lot of people would be outraged. But back in the early part of the 20th century, the term "idiot" was used as a clinical term, to denote people with extreme mental retardation. Or, maybe you'd prefer extreme mental handicaps, or mental disabilities, or people who were extremely non-neurotypical. All of those phrase have, at some point, been used as terms and euphemisms for people with Down's syndrome, severe autism, etc., and all of them have since acquired other connotations. Some of them, like "mentally retarded," have come to be seen as offensive. This is because people view of the condition of intellectual disability is negative, and whatever neutral term is used soon becomes a pejorative word due the negative connotations associated with the underlying condition.

This is what is called the "euphemism treadmill," and a similar thing has happened for terms for what I'll call "black" people (this seems to be the prevailing nomenclature currently). Since it was seen by many as a bad thing to be black, these terms took on pejorative meanings, until they became too laden with those meanings to function neutrally. Terms like "nigger," "negroid," "person of color" and "colored" have all been used as a relatively neutral description at some point, only to gain additional baggage along the way. For "negro," the main shift happened in the 1960s and 70s, as the Nation of Islam, Black Power, and other movements turned their focus towards African heritage, and the terms "African-American" or "Afro-American" became more popular as neutral descriptors.

Check out this article and accompanying letters to the editor, published in the magazine Ebony in 1967 and 68, which shows some of the contemporary debate over the term. Some of the letters show the reactions people then would have had to the terms "negro" and "Afro-American:"

http://www.virginia.edu/woodson/courses/aas102%20(spring%2001)/articles/names/bennett.htm

Anything except that odious word, "Negro," which has such a ridiculous heritage of mockery. We were not dropped into America; we were forcibly dragged from Africa. So what else are we? Words are the greatest avenue of communication and much more reliable than signs. They are forceful symbols! Words, that is. Besides all of this I have a sinking feeling that the dear old Boers, or whatever they are in South Africa, would just love to RIGHTLY own the name Africans; they tried to get as close as they could. Let us all rally around Afro-American. I think Black has connotations of arrogance.

Another brought in the historical context that "negro" is derived from the Spanish and Portguese word for black:

By choosing a term such as "Afro-American" and rejecting terms devised by muddle-headed and money-hungry Portuguese slavers of the 15th century, black people of the Americas are no different from their brothers of the African and Asian countries who, after having driven out the Western exploiters proceeded to rename the lands of their heritage.

Others weren't so sure:

I have no qualms about being identified as a Negro. I regard that designation as nothing more than an impersonal, factual description of one of the major branches of humankind. The unfavorable connotations that have grown up around the word are unfortunate, I feel, but hardly worse than those associated with ethnic names that do not even identify a race -- merely a nationality.

And Sgt. Irwin B Taylor gets to the heart of the matter:

There is no real advantage in eliminating the word "Negro." Probably before any change would be accepted widely, the connotation given to "Negro" would be transferred to the new term. then the cycle will begin all over again.

The only real solution will be the changing of the meaning of whatever term is used most today.