It turns out this is a very old discussion. There is a concept called a "lie of omission". Here's a wikipedia page about the entire concept of lies: https://en.wikipedia.org/wiki/Lie

A question for you: if you make a mistake or misunderstand something then share it, are you a liar?

I don't mean like your current actions - the part where you are pretending that you have never encountered the notion of lying like this is clearly itself some sort of lie. I mean like say you apply some math rule incorrectly on a test. Should you be kicked out for lying to the teacher?

To lie is to tell a deliberate falsehood - to say something you know to be untrue. Sometimes this is taken to be acceptable - to tell a "white lie", e.g. in response to, "Does this dress make me look fat?"

Saying something incorrect, but which you believe to be true, is no lie.