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.)
@JonKramer Also, only concrete nouns can be touched. Abstract nouns, like "idea" or "thought" or "law", are still nouns too, even though you can't touch them.
@LouisIngenthron yes, obvious in retrospect. So, nouns or adjectives. Got it.
And thank you.