Words help us not only to communicate more effectively but to think more clearly. Terms like La Raza (literally The Race) are misnomers because mestizos are not a race (subspecies, variety) but a mixed race people but perhaps that buoys-up some egos-- I don't know. Sounds stupid to me.
Most of the time, anymore, when the term "spic" is used, it is not accurate. it was a term of derision from a time when there was a lot of Spanish immigration and much of it was of mixed blood. However, some of the most beautiful women I've even met were Spanish, White as the driven snow, and had classic features, one surnamed Bogardus comes instantly to mind.
A lot of pejorative terms for racial groups didn't start out being offensive, like wop, which I understand evolved from Ellis Island mmigration officials use of the acronym for "without papers" and, since that applied to so many Italians, it stuck.
My take on how some racial terms become offensive is in how one holds their mouth when they say them, betraying their negative feelings. The term Jew is somewhat like the term nigger because it is something that Jews use among themselves but puts many of them on at least yellow alert when Whites use the term. Many Jews anymore seem simply seem to not want Whites to notice that they're Jews much less say it.
The sadly archaic term, "half-breed" or simply "breed," was useful slang, it "rolled off the tongue" (easily), and has undoubtedly fallen from use because it is now considered perjorative and therefore politically incorrect. My all-time favorite western movie is Lonesome Dove and they make good use of the term describing Blue Duck, who demonstrates both psychopathology, likely born of bitterness and resentment, and hybrid vigor-- not unlike the same phenomena of mulattoes. The book, which is more detailed, if you enjoyed the film version and want more, is available in paperback but you may wear it out: Friends from Arkansas to California re-run the DVD all the time. If you haven't seen it, rent it. I like the term half-breed because its intuitive even if you're unfamiliar with it, and few, these days, understand the term mestizo, much less mulatto or that those last two terms are not intended and are defined as offensive.
Spade, as in "black as the ace of spades," is another archaic term that was popular and inoffensive when I was in high school. It never was like nigga, something they could call each other but you (White man) couldn't use. It was used almost affectionately on the East Coast to describe, say, that spade cat Miles Davis, who played the flugelhorn on his Sketches of Spain album.
A good piece by a mestizo-Mexicano is here: http://sonic.net/~doretk/ArchiveARCHIVE/NATIVE%20AMERICAN/TheMestizo-Mexicano-Indi.html
MERRIAM-WEBSTER
mes·ti·zo -(ˌ)zō Function: noun
Inflected Form(s): plural mes·ti·zos
Etymology: Spanish, from mestizo, adjective, mixed, from Late Latin mixticius, from Latin mixtus, past participle of miscēre to mix — more at mix
Date: 1582
: a person of mixed blood; specifically : a person of mixed European and American Indian ancestry
vs.
spic variant(s): also spick ˈspikFunction: noun
Etymology: by shortening & alteration from spiggoty, of unknown origin
Date: 1916
Usually offensive: spanish american
Finally, have a look at the meaning of profane, as in profanity. One of my English professors, who also coached drama, could tell you to go to hell in a few accurate words that stunned such that one "hung on every word" and rather than primarily offending it caused one to stop and think. Such is the power of language. He was fond of saying that " profanity is the attempt of a lazy mind to express itself forcefully."
1pro·fane prō-ˈfān
Function: transitive verb
Inflected Form(s): pro·faned; pro·fan·ing
Etymology: Middle English prophanen, from Anglo-French prophaner, from Latin profanare, from profanus
Date: 14th century
1 : to treat (something sacred) with abuse, irreverence, or contempt : desecrate
2 : to debase by a wrong, unworthy, or vulgar use
— pro·fan·er noun