That you think this way (and if like me, it makes you excited!) I think it's because it has clicked for you.

For many that light bulb above their head doesn't flash on, hence they get to dislike the subject or forget it after they are done with their studies. I was lucky enough to appreciate math that much to redo it in my free time after high-school and make it click for me.

No, my calculus class in HS very literally started with finding the area under a curve “manually” and introduced integration as a generalization of that. I’m not surprised to hear that calculus is sometimes taught very poorly, but it’s not universal.