single word requests - A Noun which describes an ignorant person accusing a well-informed opponent of ignorance?

The first word that comes to my mind is uppity.

You must be careful when using this, however, especially if your opponent is black, lest ye be accused of racism.

The word was once used commonly as a pejorative term against slaves who disobeyed / tried to outsmart their masters, but its actual meaning has nothing to do with race and everything to do with status.

In this context, one is uppity because they are placing themselves in a higher position than one who is clearly more educated (= of higher contextual status) than they are.

Sources:

Merriam-Webster

Urban Dictionary

If you want something a bit more politically correct and sophisticated, try pretentious. If your intent is to insult your opponent, you may add an intensifier of your choice.