It's not just about "you should code like that because that's how we code here" type of problems. That makes you, the arrogant person in the story. You should create a list of bugs generated by his code. If the list is significant AND if you believe these bugs could be avoided by incorporating %100 of your code review feedback, then setup a 1-1 quality meeting with him and go over the list. Tell him how this could be…
IMO you shouldn't try to prove that his code is bad and the feedback is good. Even if his code is perfect and the feedback is bad, he should still respond to the feedback with a justification for his approach. If his way is really better, then he can educate his peers about it.