He resists because of fear. This conditioning may be the result of previously bad experience(s) about being reviewed, as a kid, at school, at work or even in your current team. In our modern societies, it's very common for us to confuse someone's work output with his value as an human being. That why reviews at work are not well perceived. That's also why speaking in public in one of the most spread phobia (fear of judgement).
To avoid such behavior, you will need some psychology. You must prove to his lizard brain it's not going to happen (he won't be judged, humiliated, killed, anything...) by desensitizing him to code reviews.
One of the most effective method I found to unblock someone is to ask him to review your code, before asking to review his code.
After a while, propose him to read his code to learn from it and why not suggest improvements. When you find something to change, be careful in what you write. He will understand there is nothing to be afraid of, and he will take the positive part of the reviewing process only: learning and increasing his knowledge.