I don’t really need to explain the meaning and derivation of this word, do I?
“We’d like to invite you to… no longer live with us,” as the lady in the movie said. Or, on a smaller scale, “You are cordially invited to leave this party.” “Hope you enjoy no longer being around here!” And the classic line that the waiters at our annual Christmas party (back when I worked at a company) loved saying at midnight, “You don’t have to go home, but you can’t stay here.”
Yes, just as out is the opposite of in, outvite is plainly the opposite of invite. Never mind that Word will change it to outvote every single time you type it (until you tell it to stop); it’s plainly a word, and an obvious one. (And anyway, you’re often outvited because you’ve been outvoted. There are a few politicians who know this. Many, in fact.)
Yes, yes, invite comes from Latin, invitare. So you might think that since Latin for “in” is in but Latin for “out” is ex, its opposite should be exvite. However, there are a few reasons this is not so.
First is that ex is not used everywhere; in many places, including prefixing consonants, it’s e, as in e pluribus unum(which means “out of many, one,” i.e., “there are many of us here, and one of you, get out”) and egress. Using this morpheme, the converse of invitare should be evitare.
Second is that evitare is a Latin verb, but it means ‘shun, avoid’ – a sort of self-outviting, you could say. It has survived in English, not as itself but as part of inevitable.
And third is that outvite is a perfectly cromulent word, so lay off.
There remains the question of whether outviting is brusque or diplomatic. Diplomacy, to borrow a line not from Churchill, is “the ability to tell someone to go to hell in such a way that they will look forward to the trip,” so it would seem apposite, but we know very well from experience that some outvitations are more on the order of ejections. There are a few websites that give definitions for this word, and their definitions disagree on this point, but none of the sites are the dictionaries of record (yet). So the currents of usage will have to sort it out over time.
And if you are outvited? Surrender to the inevitable – to quote the other classic line, “Don’t go away mad. Don’t go away sad. Just go away.”