I can really relate to your experience, even though mine was from a parent's perspective rather than as a teacher. I found a similar thing when tutoring one of my children in trigonometry. The way the material was being presented in school didn't click with him, but astonishingly, despite having studied it decades ago both at school and university, explaining it to him, it finally made sense to me. The unit circle definition of a tangent is a thing of beauty. I had the time to get my child to appreciate it as well, because of the extra time I had to spend with him, whereas the teacher had to hit curriculum benchmarks.

I also think this is where things like intergenerational math-phobia come from: parents who don't grasp core concepts and are scared off, and can't help their own children, creating an ongoing cycle.