"Paul's Case: A study in Temperament" is, as the title states, an analysis of the sensitivities that are unique to a curious young man whose dissonance with his environment creates the sad reality of his life.
The exact causes of Paul's odd behavior are not meant to be explained with a medical term, or with a social label. This is why the story is labeled as a "study", and not as a "biography". By "study", Cather implies that the process of analysis is ongoing, and never to be finalized with a "diagnosis". It also entails that Paul will also continue to change and expected to get either better, or worse.
Paul's main problem stems from a social disconnect. This disconnect is aggravated by his extreme sensitivity which, itself, is further aggravated by his environment. As a result, Paul seeks in the mechanical, in the plastic, and in the fantastic the aesthetic ideal that he could never reach if he were a typical young man of his age.
The paragraph that gives evidence of this and which explains Paul's condition the best is the following:
Perhaps it was because, in Paul's world, the natural nearly always wore the guise of ugliness, that a certain element of artificiality seemed to him necessary in beauty.
Here is a symbol of the aesthetic mentality which permeates Paul's behavior. Paul's sensitivity (one which is quite heightened) seeks beauty in all its respects. Therefore, since the natural world with which he cannot connect does not provide him what he seeks, his most natural reaction would be to seek it in the artificial palace that is the Carnegie Hall.