Probably a bit of both. It was only after observing my cousin's son for a bit and hearing about what he liked that people began to remind me how tenacious I was, and really many others in the family. I'm pretty convinced that if I had only been introduced to calculus before becoming a teenager I wouldn't have given up on mathematics so easily. Kids are capable of a lot more than we're willing to admit– I say it's part insecurity, part genuine fear of being 'wrong', expecting too much, etc. thereby helping your kid fail.

The intuition of game theory is instinctive part of human nature and primates in general. It only gets hard when you do sophisticated calculations. Kids learn how to ride bikes too, but the physics of gyroscopic motion is hard.

It wasn't until 11th grade phyiscs that anyone bothered to explain what derivatives and integrals are, let alone how to calculate them or what they might be good for. Let me reiterate: it took until high school physics, twelve years into my math education, before someone showed me that calculus is the best/only tool for answering questions about nature, and that all the algebra crap matters because you can't do calculus without it.

Fourth-grade me had intuitively latched onto the idea that a curve's slope must itself have a slope. Limits (at least 11th-grade precalculus level limits) would have been well within my grasp in elementary school. In "helping" my dad with a basement remodel, I had actually wanted the area of a shape bound by a curve, but had no idea how to proceed. I developed an elementary understanding of recursion in my PHP and Python-hacking days (elementary and middle school - no time for that now) and had no trouble with time-complexity, object orientation, or introductory functional programming. NONE of that was so much as hinted at in school until sophomore year.

I don't know why we treat these ideas like dangerous weapons whose existence can only be hinted at until one comes of age.

I am a much better thinker than computer. Because my experience with "math" was years of drilling arithmetic, doing long-form multiplication and division without a calculator (WTF?), converting between forms for lines and parabolas, finding the x- and y- intercepts, plugging and chugging the quadratic formula, simplifying/solving nasty algebra, etc, I hated it. Nobody bothered to show me the point, I got sloppy, and now I'm sitting here with A-es and B+es throughout high school math, 660 on the SAT math section, 26 on the ACT math section (not outrageously difficult conceptually but a high-pressure speed trial), and no shot at any decent university's computer science program.

I think society loses a lot by making elementary/middle-level education about drilling exercises instead of engaging students with ideas to think about with the mechanics treated as secondary. Especially at the elementary level when kids are still naturally curious and have time and energy left over after school/homework to think and process. If I'm exceptional, my grades and test scores don't show it - I think a lot of kids could have handled substantially more on the ideas front.

Also: Shortly after learning to read in kindergarten, I was reading well above "grade level." Either I was innately gifted or "grade level" is pathetically low. I don't mean to disrespect the education experts, but it seems I've been helped orders of magnitude more, even at 8 years old, by the ambient presence of public radio, reading "grown-up" books and news I found interesting, and participating on internet forums than by identifying subjects and predicates or regurgitating plots onto tests. (Forced practice of composition is good - I've seen it help good writers get better, but I've never seen a bad writer improve through schooling).