To be thersitical is to be like Thersites (you say that therSIteez).
Thersites was the ugliest member of the Greek army during the Trojan war. He was also evil-tongued (though what he said was sometimes what everyone else was thinking but had too much sense to say out loud).
That ugliness and being horrible should go together is no surprise: a lot of ugliness is nastiness glinting through.
But times have changed since the Trojan war, and with the advent of the internet it is possible for everyone to be beautiful - online, at least - and yet it's still the easiest thing in the world to be evil-tongued.
Perhaps we should remember the fate of Thersites, who was killed by Achilles after Thersites mutilated the corpse of a hero.
And it's really quite hard not to say that it served him right.
Thing Not To Be Today: thersitical. This word comes from the name of the Greek soldier Thersites. Homer implies he was a common man, but another source who mentions him says he was a prince.
Both can be equally foul, so I can't see that it matters, much.