Banter by definition is teasing, which insulting. That, along with being humorous in that context and not to be taken seriously is what makes it banter rather than any other form of exchange.

Lets just go to the dictionary:

Banter (n): the playful and friendly exchange of teasing remarks.

Teasing (adj): intended to provoke or make fun of someone in a playful way.

And in specific, "not even wrong" is a total shutdown, not playful.

Oh I agree 100%, that wasn't banter, it was a grumpy shutdown.