My biggest frustration learning math when I was younger was not knowing -why- I was doing something a certain way or how it worked. It was incredibly discouraging because it didn’t just “click” like it seemed to with my peers.
It's a very healthy mindset to have, but it's a blessing and a curse. Some people are just very good at just abstracting away the details and getting on with things; what seems like "clicking" is not always the same as intuition. Probably it's good to operate in both modes. It's a really really useful skill to know when you need to care about the internals and when you can safely ignore them.
Arbitrary example:
One teacher kept saying "f(x)" but couldn't explain what a function is. He just said "it's anything", then "don't worry about it". If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok.
I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was.
Helpful but not quite right and one of the common misconceptions students seem to carry over from high school.
A function is something that takes inputs out of a set (its domain, e.g. people in this class) and gives you exactly one output with a prescribed data type (e.g. a date. The function than for instance being person -> birthdate). Neither numbers nor a formula are needed.
> I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was.
I think he probably could, but the syllabus said explicitly not discuss this ("too abstract") and there is time pressure. High school maths mostly is somewhat handwavy and stringing "definitions" together by examples. So you would mostly see lots of examples of functions and the "definition" of 'function' is then simply "things like that".
I was the same as how you describe yourself, and I always just assumed the kids who were best in the class were doing what I was trying to do also, but were much better at it. And then you see later how fragile/limited one's understanding is when taking the memorization approach—but as a kid you don't have many options.
Schools tend to not teach mathematics but memorization, unmotivated formulas and computation. Mathematics as its own discipline is basically only "why and how", i.e. proofs.