When I tell people I study physics, more frequently than not I've had to help avoid a panic attack or two. There's always that 2nd grade teacher, the trauma, the gnashing of teeth; I don't really fault people for having gone through the pedagogic wringer and suffered the tyranny of schooling. This is the story I tell math-phobic to let them know I think they're right.
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Let's imagine an you are in an ideal art classroom for beginners in secondary school. The recess bell rings and the kids are streaming in to their seats. In front of every kid there's a full decked-out art kit: brushes, paints, canvas and the works. Being their first art assignment, the kids will fill out one of those paint-by-number Monalisa's – there's chunks of the painting numbered 1 and they should all be green, all the 2 sections should be red, and so forth.
The brushes begun to dip, swirl, then dance across the canvases and the kids are jubilant. You've been completing the green->1 chunks when a hand strikes your fingers holding the brush.
Sorry kid we're in art class, and, in here, when you paint green stuff, you must do it always by holding the brush with these two fingers at a time, and you must stroke from left to right
Apoplectic, you ask "Why?"
Because I said so, and these are the rules for art.
...
You muster what courage you can and soldier on with the greens. Remember your parents' edict: failing this art class will mean detention, do overs during summer break, getting grounded - not a fun way to spend vacations. The teacher isn't too worried about explaining why these rules of art must be so, but questioning aesthetics isn't really proactive in the present situation.
Halfway through the reds, a swift hand strikes down your brush again:
In art class, when you paint the reds, you must use these other two fingers, and always stroke from the top to the bottom.
"How was I supposed to know that?"
Doesn't matter. Shape up or you'll fail this quiz.
...and you figure this will continue for each other color. The lesson is clear - disobey and be punished for failing these rules obtained from god-knows-where, so it's best to try and suss them out piecemeal from the teacher and avoid their wrath.
But every torment must end, and though there's been wailing and gnashing of teeth, your Mona Lisa is finished.
The teacher comes by, pops up your piece into the sunlight and delivers the coup de grace:
Ah! Look at this beauty - isn't art just beautiful?
My claim is twofold: any child that walks out of such an "art" class saying they like art is in need of a dire intervention and/or therapy, and that (modulo metaphoric license), that is basically how we teach "math" in most schooling systems I know (or rather arithmetic).
We show little empathy with kids about why they're learning a particular system, punish them based on our predetermined system of axioms without explaining why we chose such a system over many others, and people just learn to game the system enough to evade punishment (we're only talking about harsh impacts to your future economic prospects here!).
Why are we learning about these numbers and not others?
Because they build up to calculus and we've "decided" as a society that that goal is what will make you most productive.
How do we know these are the only kinds of numbers that have these rules?
There might be many! But you better learn these or else!
Why not choose different rules for our numbers? Why not have different axioms for our geometry?
We'll have none of that nonsense here you lil' insubordinate rascal...
Do we really need to optimize those missile trajectories?
Alright, that's enough thinking about where the tools we teach end up being applied.
...and so on.
Yes: some form of rote practice is needed to gain basic mathematical acumen - but nowhere near the level of attention that it deserves. Spelling drills are necessary to manipulate language, yet spelling bee championships do not poets make; neither should we conflate arithmetic worksheets and piles of homework with exercises in mathematical thinking.
Worst of all, I think is that people don't even have the vocabulary to know the worlds they aren't seeing. This is in contrast to musical experience - even if you never hit a solid note on your recorder, you can still appreciate songs and dance beyond your classroom disappointment. But how would you explain to someone that Daft Punk, Dolly Parton and Beethoven can coexist in the same universe of musical enjoyment if their (let's imagine for sake of argument) only musical exposure in life were the beeping of an alarm clock?
You'd get a lot more people traumatized about art and music class, and if I was a musician in that world, I'd also field a lot of people dumping their childhood traumas on me because I was "into music".