If it is of any consolation. You are spot on, and saved me the effort (which had run out). I'd recommend to leave it alone as well, as it isn't worth it to try and explain logical fallacies. Or, heck, you do you. I'm just too old for it
If you really want to play this whole "logical fallacy" game, then I can start demanding sources and specific definitions of words used too and you can spend hundreds of characters defining specific terms so that your own discussion points aren't themselves some variation of a "logical fallacy".
Folks who toss those things around usually don't know how to use them correctly (as we see here with you and others) or they hide behind them when their various points are met with challenges they can't overcome.