That is possible, but it is unwise to bet that way.

Why?

First, because far more things can be explained to an intelligent lay person than most of us realize, and figuring out how to do so improves our own understanding. Therefore it is worthwhile to make the attempt.

Second, because it is far too easy to fool ourselves into thinking that we're making a succinct explanation that requires domain knowledge when actually we're spouting just enough jargon to remind those who agree with us of shared and possibly unexamined dogma. There is a real cost to mental habits that make such mental mistakes easier to make and sustain.

So yes. The other person may be too ignorant/stupid/whatever to understand you. But the alternative explanations should be disproven before you conclude that.

It's a classroom setting so the discussions are between peers with similar knowledge.

It is even more true in the real world when the discussions are between people with different knowledge. Do people recognize someone from another background as a peer or not?

If all parties are interested in the discussion they can ask questions to fill in gaps in the knowledge. Doesn't always happen of course.