Don't explain to the student why he is incorrect; place the burden on him to demonstrate that he is correct.
Propose a deal with the student that would give him most of the power by conditionally accepting that you are wrong. Tell him that you're willing to hear his side, admit that you are wrong and reconsider your marking of his assignment on the conditions that he:
(1) explain to you, in a comprehensible way, with facts and plain English (not hypotheticals, slang or colloquialisms), why you are wrong; and
(2) show you some empirical, verifiable, credible evidence to support that his answer (that you marked wrong on his assignment) is correct.
This gives him almost all of the power, but also places on him a burden that he will likely fail to meet. If he actually does meet this burden, then his answer should be marked "correct." In all likelihood, though, he will have no choice but to accept that he cannot explain to you why you are wrong and cannot show you any evidence that his answer is correct beyond, "I'm correct merely because I say I'm correct." Unless he suffers from some mental incapacity, he will understand (even if he won't admit it) that the failure is on his part and not yours. If he thenceforth continues asserting that you are wrong, you can remind him that you gave him an opportunity that he chose not to take or failed to bring to fruition.