Insults are not a part of speech, they are a tone of speech. The specific phase could be declarative, interrogatory or even an interjection. (e.g. -"You're stupid" or "Are you stupid?")
An derogatory epithet is usually a noun or a noun with an adjective or some other modifier.
It is usually better to characterize what a person says or does, rather than name calling when you need to critique their actions. (e.g.- "That was a foolish thing to say", rather than "You are a fool.")
(I assume this was a legit question, and not just a setup for the joke at the end of your toot.)
@Pat , not a setup for a joke, legitimate question. You say insults are nouns... I am resistant to that because they can't be touched... which is how I learned what a noun was back when Eisenhower was just a butter bar. You can touch a buffoon, for example.
But, I'm a math guy, not English. And I know it.
@LouisIngenthron yes, obvious in retrospect. So, nouns or adjectives. Got it.
And thank you.