When something appears a certain way, but is also its opposite

Solution 1:

With regard to your analogy, I would not equate the need for solitude as the mark of an introvert. In my experience, extroverts get energy and fulfillment from interacting with others. Introverts gain energy and fulfillment from themselves. Both types may interact, but in the interaction, the extrovert gains energy while the introvert looses it to the extrovert.

Now to your question. I think oxymoron is an excellent choice but connotes foolish rather than just opposite. It may also be an absurdity but if the analogy is real or based on reality, I would want to say it is a paradox.

Solution 2:

You could say the outcome would be paradoxical, or that the outcome would present a paradox.

Paradox (noun)

• someone who does two things that seem to be opposite to each other or who has qualities that are opposite. (M-W)

• A counterintuitive conclusion or outcome. (Wiktionary)

I think oxymoron would be incorrect, as an oxymoron happens when words in a phrase contradict each other. This is not the case. Instead, the person has two personality traits that clash with each other. I think this is a classic example of a paradox.

It's also worth mentioning the difference between a paradox and a contradiction. A paradox is something that holds true in spite of a (seeming) contradiction. A contradiction is something that can never hold true, since it's necessarily false.