We definitely should see if we can develop math teaching which doesn't elicit that response, because it has to be learned. Humans aren't evolved to be good at arithmetic or symbolic thinking, but we're not evolved to be morbidly afraid of it, either.
Of course, any attempt to improve math education gets screamed at ("New Math! Common Core! Blah!") and the whole thing just becomes political.
I think we just have to accept that we all are different. Some have it easy, other don't. This comes doubly with all subjects that we are not trained for or not interested in. It might take a lot more to learn or a teacher that understands the problem and can guide around it. Only the individual can say if the added time and effort is worth it. This insight can take many years though, it's hard to get a teenager to believe they will ever need math (or whatever other subject) in their life.
Part of the problem is cultural - it's socially acceptable to "not be a mathsy person" in many circles, and almost a badge of honour in some.
Another problem is that the discovery learning approach can lead to some horrible failure modes for math. I've seen cases where an hour of proper instruction can go further than a whole term of trying to see if they can find it out for themselves. Case in point: the rule of three. If 10 apples cost $20, then 5 apples cost ___? You can spend ages thinking about what it "means", or you can learn that you write down a 2x2 table, multiply across the diagonal and divide by the number in the corner.
Commom core seems just fine overall to me. I wouldn't be surprised if the generation that grows up with it has much better math comprehension and number sense.
Of course, any attempt to improve math education gets screamed at ("New Math! Common Core! Blah!") and the whole thing just becomes political.