I think you put your finger on a challenge fundamental to teaching itself. Speaking as a (former, at least for now) teacher, the concepts that I find most intui

I think you put your finger on a challenge fundamental to teaching itself. Speaking as a (former, at least for now) teacher, the concepts that I find most intuitive were always the most difficult to teach, whereas skills I struggled to master were the ones I was best able to instruct. For problems in the second category I could diagnose the gaps in my students' understanding or application - likely because I'd faced them, or similar, myself - and strategize an approach that would help. Conversely, the subjects that I "got" without effort, left me floundering (at least at first) to find an alternate way to present to students. (I suppose that's where the terrible canard of "those who can't, teach" comes from. There's a kernel of truth to it, of course, but the more generous and relevant point is that success through effort is better preparation for teaching than success through natural ability alone.) My guess is not that your teacher would disagree that math is "a fundamental language of the universe", just that she spoke it so fluently that she wasn't well able to relate to people who don't.