We’re trying to show that people with doctorates in liberal arts are rarely hired. To do this, we want to show that people with doctorates in liberal arts are not interested in financial gain. Learning what happens to people with doctorates in liberal arts if the ARE interested in financial gain doesn’t establish that these people are NOT interested in financial gain.

We don’t know whether people with doctorates in the liberal arts are among the “some people who are interested in the liberal arts” in this answer.

“The only” introduces a sufficient condition. (”Only” without “the” before it introduces necessary.) So (C) tells us that IF you’re not interested in making money, then you’re interested in improving intellect. But this reverses what we want. We want to know that if you’re interested in improving intellect, then you’re not interested in financial gain.

(D) doesn’t establish that people with doctorates in the liberal arts are not interested in the financial gain of the business world. So it doesn’t prove that people with doctorates in the liberal arts are rarely hired by companies.

“Only” introduces a necessary condition. So (E) tells us that if someone is interested in improving intellect, then that person is not concerned with making money in the business world. This provides the missing link between the two premises, which allows us to conclude that people with doctorates in the liberal arts are rarely hired by companies.