Jackass v. Jackass: Muslim Trump Supporter Twitter War Edition

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The party of the first part (background info: a female Muslim immigrant) writes a predictably facepalmerific pro-Trump thing in the WaPo, filled with typically bad reasons (and also at least one plausible reason) for voting for Trump--as is her right.
The party of the second part (background info: a prof at Georgetown) loses her Twitter shit and FTFO out in response, "tweeting" (facepalm at this stupid word that I will never be able to type with a straight face no matter how many times I make fun of it) all sorts of stupid, fantastically out of line shit to her in response.
Biggest jackass at this point: the party of the second part, and no contest.
But wait! There's more!...
TPOTFP then writes to (in effect) the Chair of TPOTSP's department in what seems like an attempt to convince the university to discipline TPOTSP in some way. Whaaaaa?
Wow! The part of the first part is now the biggest jackass by far! Betcha didn't see that coming!
Georgetown issues a milquetoasty reply that references the First Amendment...but does not slap down the nonsense in the way that it deserves to be slapped down...so we'll see.
These two people are both jackasses. But the offending Twitter exchange was between these people qua private individuals. It's none of Georgetown's business. Am I missing something here?

(h/t the redneck raconteur)