People here are saying math is hard, math is non-intuitive, math is useless in real life, math is not taught in a fun way, etc. I disagree that these are the reason behind math's lack of popularity. They're very superficial, and mostly a consequence and not the origin of the problem.
Background: I've been making educational math and physics illustrations for the past 10+ years. I've tutored a few people as well and I've worked on some other educational multimedia projects along the way. A lot of my work has been praised for being clear, intuitive and "more helpful than years of classes". So judging from the response of others, I'd say my approach to math/physics education has some merit.
Now, as others pointed out, this is not really an issue with the US. The lack of appreciation for mathematics is widespread and nearly universal.
I was brought up with the world view that the world is out there to be understood, if only we pay attention to the way it expresses itself. My parents taught me that math, physics, chemistry, biology and etc. are just different ways to understand how different facets of the world around us work.
So from the beginning, my parents taught me and my siblings that the world could be made sense of, and if we put the effort in it, we could understand it.
Humans are naturally curious. Children in all cultures universally ask "why?" questions to the exhaustion of their parents's willpower to answer. The usual response is to eventually curb that curiosity for the sake of simplifying the worldview of the children and simplifying the lives of the parents, who get sick of indulging in that curiosity after a while.
This is a huge mistake.
This worldview that "BECAUSE IT IS" or "BECAUSE X SAID SO", when taken to heart, naturally inhibits the predisposition of the person to invest in understanding or knowing things. I can't cite studies on this, as I've never heard of anything of the sort being done, but from personal experience people who excel in math and physics (or science, in general) are just very curious people. If you ever dealt with kids asking questions, you'll notice that the curiosity in these people just didn't wear off. It has the same flavor.
That curiosity survived because it was rewarded over the years, and the reward for curiosity is wonder. It is exciting to figure things out. But we use the expression "childhood wonder" almost derogatorily these, as if it is naïve to be amazed and excited about things.
So one thing you can do to your kids is merely to indulge their curiosity. Give them the worldview that there's stuff to figure out, and there's ways to obtain answers if you don't know things.
When they ask something you don't know, don't say "it just is" or lie. Admit that you don't know. Say "I don't know, but we can find out!" and make it an activity to do together, or help them do it themselves. Go search online, or make experiments, give them the confidence that they have the power to figure things out.
Now, with the proper mindset in place, these kids will face a very different and unenlightening approach when they finally get to study in a school environment. Due to time, knowledge and social constraints, kids will inevitably get a pretty shitty and superficial education, in math or anything else.
But what makes math particularly difficult is that it adds up, it builds on top of itself. If you never understood geometry and algebra, trigonometry and calculus will become fuzzy and weird.
When math is properly understood, every next step is sensible and makes perfect sense. This is exactly the inverse of the perspective everyone seems to have, which is a tragedy on its own. This is clearly reflected in the other comments here.
My point is that math IS intuitive, by default, and when you think it isn't it's your intuition that is wrong. This means your understanding of some aspect of math is incomplete or incorrect. Mathematics is just a series of logical steps with a clear intent, and this is something everyone should be convinced to be true.
It seems to me that the origin of this whole hate affair with math and physics lies at the way people approach the subject.
Math and physics are taught from the perspective I call "this thing exists". This strategy basically pulls a concept out of thin air, plops it in front of students and have them memorize the fact that concept exists in so and so way. Then they plop another concept and explain a rule, that was also pulled out of thin air and also needs to be memorized, that connects both. This goes on and on, until your entire mathematical framework is a collection of impenetrable and incomprehensible rules and jargon.
So it's no surprise people would claim the whole thing is hard and useless. Memorizing abstract rules and weird names is hard, and it feels pointless. Trying to shove real life situations in the middle of that framework is not going to help at all, and it doesn't.
The CORRECT approach should be from the perspective I call "we need a thing, how do we do it?". Now, mathematically oriented people will already be complaining to me that "teaching kids formal proofs? are you nuts?!" but I'm proposing nothing of the sort.
I think formality should come second to intuition. It's much easier to build formality on top of intuition than intuition on top of formality. Intuition is also more useful, especially in the long term: you may not remember how to compute the area of a circle, but if you remember you can cut a circle into several tiny triangles, you can quickly derive the area yourself.
So, for instance, instead of telling people a circle has 2π radians, show them why and how to build a radian, and show them how half a circle has around 3.141592... radians, and how we can simply call this number π to simplify things. Immediately, it follows that 2π radians cover the whole circle, regardless of the size of the circle.
Want to explain why cos2 x + sin2 x = 1? Explain to them what cosine and sine are in terms of the unit circle. They'll understand that cosine is the horizontal position of a point at x radians around the circle, and that sine is vertical. They can now immediately understand why sin(π/2) = 1. If they understand this difference between sine and cosine they don't have to remember SOHCAHTOA because it's obvious from the construction.
The entirety of algebra is about creatively doing things to both sides of an equation, usually adding zero and multiplying by one in creative ways. This is ridiculously obvious: if two things are equal, doing the same thing to the two things shouldn't change anything! Nobody has a difficulty with this concept. Instead, people are taught to think of meaningless rules to move symbols around, and the underlying concept of algebra is lost.
Every single concept in math can be taught from this approach (and it is, but formally in higher education). It is not done this way because most of the times the teachers don't fully understand the concepts themselves, and also because the mathematical literature is ripe with regurgitation of old teaching techniques. (Which, I think, it's about time we get rid of and start from scratch with modern tools.)
And mathematicians and physicists are to blame as well. Things are often deliberately made more complicated than they are, almost as a way to show off how much smarter they are than the student who's trying to learn for the first time.
Teachers forget they once were students themselves, and the pitfalls and mistakes they've made. If teachers were a little more self-aware of this, math and physics education would improve tremendously.
(EDIT: This last point is what I try to keep at heart when I do my animations. When you finally understand a concept, when something finally clicks in your head, there's usually two responses: excitement, followed by anger. We always think "Aaahhhhhh! Of course! This is so obvious now!", and a second later, "Why the HELL did nobody tell me that from the beginning?" So I've been telling things how I wanted them to be told from the beginning.)
So there's a huge amount of variables at play, and unfortunately, they are all in a feedback loop. It goes way beyond math too.
It will be hard to change things overnight, but one way to start is to sell people this simple idea: it is fun to figure things out.
Mathematics is just a puzzle game. People enjoy puzzles and games, one way or the other (all areas of human knowledge are about piecing together a puzzle of some sort.)
They just haven't learned to see the puzzle in math, and they don't know how to play it. It's as if we're teaching people how to paint by showing them famous pictures, or how to compose music by having them listen to music.
If you realize this, it's no surprise people don't enjoy math: they were never taught or allowed to play the game.
There's a famous text by Paul Lockhart about how the beauty and fun in math is lost to most people due to poor education. It's too poetical for me, and not exactly offering solutions, but it's well worth a read.