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I think this is true for lots of people. I also think there's a bunch of us that have never had that feeling of it being a memorisation task.
In fact, the reason I liked maths and science was because it wasn't memorisation. Unlike languages (for example) you could always work out the bit you forgot, and didn't need to depend on some made-up aide-memoire that only applied 75% of the time and remember what 25% it didn't apply to.
All I can think is that some early teacher failed you, and didn't lay out how the foundations worked.
if the foundations of mathematics are dependent on a single early teacher.... that's a serious dependency for mathematics then.
The foundations of everything are dependent on those early teachers.
This is true in all cases. The proof is left as an exercise for the student.