How and why is magic irrational?

[Triplicate]

My quest for a magic system, take 2.
http://www.cartographersguild.com/sh...ad.php?t=21353

One of my principal worldbuilding projects (even if I've mostly set it aside for several years) is a gonzo adventure setting. It's meant to make all sorts of stuff make sense that usually doesn't when I see it in fiction. Because it's an alternate Earth intentionally convergent with our own, its map won't be much different. The whole point is to justify certain tropes.

The planned "present" for the setting, the point in which I intended to set stories, is some point in the relatively near future. In some aspects, technology advanced faster than in our world.
Magic exists and always has. There has never been a Masquerade because it doesn't make sense. Yet societies nearly identical to those of our Earth developed. Magic did not become a science or an industry. Why?
Magic is not just spells cast by wizards. In fact, it's more likely to appear in other things; artifacts, places and creatures.

At one point, I said I wanted magic to be marginalized. I thought more about that and realized how perfectly that describes what I expect.

(You may notice that these descriptions are written from the perspective of a white westerner. I can't help that. It's based on pulp and comic tropes. I don't want to be racist, but I do view this world more from the perspective of a (white western) inhabitant than from an abstract top-down view.)

Most of what I want from magic can be summarized as "Science is logical and rational; magic is not."

I decided to repurpose my old "Magic has declined" assumption. That's no longer an objective view of the world, but a common perspective of the people who live in it (in western countries, at least).

Fitting trope expectations, the shaman of some indigenous group is likely to be a real magician. Why? Or more accurately, why isn't there anyone equivalent in European(-influenced) cultures?

(Note that I've so far ignored or avoided directly addressing the relation between the world's religions and how magic functions.)

Because there isn't. I'm not being tautological. It's that there isn't in real life, and this type of story relies on the world converging to real-world outcomes in many ways.

It's not that any color of human is any less magically inclined. There are many people in Western societies who are attuned to magic and capable of using it. It's that they're marginalized.
This arose when I thought "Who else do I expect to be a magician?"

We all know Hitler was, or at least interested. (Again, comic book conventions.) I expect Dali was; he'd been places and seen things most humans never would.
Someone with prophetic abilities isn't necessarily rich or powerful from their use. He might just be the old hobo who predicts the outcome of the hero's exploits and says afterward, "Told you so."

I realized "marginalized" is exactly the right term for the common factor here. These are people who are, or might be regarded as, crazy. They don't hold 'ordinary' jobs. Then I put it together:
In Western societies, there are still many people who know magic to some extent. They're scattered in various positions because "magician" isn't a job description anymore. For a long time, the medieval church repressed magic. Then science was developed, and it couldn't understand magic. So by modern times, there was no place left in Western societies for magicians.
We're long past burning witches. The likeliest reaction to a magician is "Why don't you do something useful?" Most people simply don't get magic.

Magic users are, in general, not rational people. For some reason, it must be irrational to place your trust in magic, even though it demonstratably works.

Magic is a disruptive force, something on the fringe. It resists institutionalization because institutions resist it. People in power are more likely to be rational, and getting a group of people to agree on something can produce decisions more rational than any individual member.

The best example I have: Soldiers sometimes carried charms to ward against bullets. Some of those worked. Yet armies generally did not issue lucky charms as equipment. Why? Maybe they can't be mass-produced for whatever reason, but more fundamentally... Strategists and administrators tend more than anyone else to be rational, so war plans don't rely on magic. Only if someone extremely irrational happens to get in power (see above) might you see a nation relying on magic strategically. And even then, remember what the tendencies of Nazi occultists in fiction are: single big artifacts or rituals, not mass-produced magic.

It's all starting to come together, but the most important piece is missing. To make a world that justifies these conventions of magic, I have to answer "Why is magic irrational?" My worry is that this reduces to "Magic only works if you believe", one of my most hated tropes. Yet I know I want one's personality and worldview to limit magic. I don't think of it solely or even primarily as "You can't use magic if you don't believe" but "You won't use magic if you don't understand". The goal and expectation is that thinking, or learning to think, in a way that makes one a good scientist, or a good businessperson, or a good leader impedes one's ability to understand and use magic. The issue might not be magic but human nature, and that's what I'm worried about. I'm concerned the stories I take inspiration from operate on some faulty assumptions about human nature. In this case, that most people are highly rational and have a need to understand things. (It's less strange than the old comic book assumption that good is default and evil an aberration...)