I read the phrase "USA intellectualism: a mile wide, an inch deep". What does it mean?
It doesn't matter whether it's intellectualism or something else, what you need to understand is the meaning of "depth" and "width" in the context of knowledge or expertise.
A depth of knowledge or understanding, is knowing all the fine detail and nuance of the subject.
A wide, or broad, knowledge, is knowing the basics, but on a wide range of subjects.
So, if I can write "hello world" in 100 programming languages, my knowledge is broad. If I can write a complex program in Java, my knowledge is deep.
If I can play "Jingle Bells" on any instrument, badly, my expertise is broad / wide. If I can play a difficult piece, beautifully, on guitar, my expertise is deep.
"USA intellectualism: a mile wide, an inch deep": A mile is very wide, compared to an inch. They are saying that US intellectuals pontificate on all kinds of subjects, but the are not looking at the details.
"Deep" in this sentence refers to the amount of thought and information contained in one's ideas. "Wide" means
So the idea expressed in this sentence is that Americans as a whole have many ideas or positions, but those ideas are poorly thought out and not backed by evidence, reality, etc.
Is it true? That is a different question.