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That's ad hominem.

Ad hominem is "you're an asshole and that's why you're wrong", not "you're wrong and that makes you an asshole".

That's a nice and pithy definition. Mind if I use it?

I wouldn't be surprised that in addition to your ad hominem philosophy, you were also an uneducated toad.

I'll have you know that I earned my degree at the finest toad university.