> it led me to realize that I had no idea what a differential equation is

I remember how I realized that I had no idea what a differential equation is when reading W.L.Burke book "Applied differential geometry" (highly recommended). Modern differential geometry turned out to be the strict mathematical bedrock for a lot of undergrad math. I was even more surprised to learn that a lot of my former teachers wasn't really aware of that.

In my view, the introductory math courses are supposed to just introduce the basic vocabulary, show the big picture and demonstrate the usefulness of the subject by showing algorithms for solving typical problems. It is not supposed to make sense on deeper inspection - and, I believe, teachers should be candid about it.