Trivializing it like that will help hide the true situation from you. Look back on the twentieth century. Find the five largest slaughterings of human life. Intellectuals claiming to be in the service of high intellectual ideas will show up in at least two of those (Stalin's farm purges, Mao's political purges). Hitler's purge would be debatable, though I'm willing to agree that simply fancying oneself an intellectual is not the same as being one. Some of the other largest slaughterings that don't make the top five, but still involve hundreds of thousands to millions of deaths, have intellectual roots.
That's just one example of the problem, I could go on. But those examples alone are sufficient to establish my point.
While it's true that America's distrust of intellectuals has blurred into a distrust of learning, there is a kernel of truth there. Intellectuals have a great failing that has cost millions their lives and caused misery for billions more, which is trusting their beautiful theories too much, even when reality is smacking them across the face with the fact that the theories are wrong or not working. (For the love of Pete, some "intellectuals" still study Marxist economics as if it has some sort of bearing on reality! Studying it for historical reasons is one thing, but not as if it's real.) Distrusting intellectualism is not a sign of irrationality; in fact I'd go so far as to say too strong a faith in intellectualism is rather the irrational position. If the 20th century taught us anything it is that reality is irreducibly complex and the beautiful-but-invariably-oversimplified theories beloved of intellectuals can not possible capture reality, but this lesson doesn't seem to have filtered out of the mathematical domain very well.
The problem is that to really understand what's going on you have to detach "learning" from "intellectualism". I like learning, I distrust intellectualism and still see no overwhelming reason to start trusting it.
We're in the middle of one failure of intellectualism even as we speak, as the global warming consensus falls apart; I don't know what truth will replace it but I feel very confident it will be much more nuanced. That came close to beggaring the entire world in the service of an intellectual theory. And more quietly, IMNSHO we're in the middle of the intellectual dietary consensus falling apart. And if I'm right about that, you can chalk up tens of millions of premature deaths and hundreds of millions of people in unnecessary fat misery into intellectualism's column, in the service of the simple-but-wrong theory that the body can be modeled as just a passive rubber bag.
That's hard to get across to a large mass of people, of course, and easy for it to get blurred. But if you don't understand this, you won't understand the real reasons for the anti-intellectual strain of American thought. It isn't just "we hate dem dare learnin' folk", which is just an excuse for not understanding.