I agree with PPs.
He didn't listen to a word she said. He has zero interest in taking no for an answer, and is trying to argue/browbeat/guilt her into dating him. His response to any of her reasons was "No, you're wrong and I'm right." That's a HUGE red flag, and even if you're madly in love/lust with someone is a reason to run away really fast.
The only sensible option now is to cut ties with him. I 100% do not think a healthy friendship is possible now. If she tries, she will be telling him that she's okay with the way he is behaving (and from the OP's description, I don't think she has the ability to both enforce reasonable boundaries *and* interact with him.). Don't answer his emails, don't answer his phone calls, if necessary, avoid things like the wine bar where he can easily corner her. At a group event - warn a friend or two that he's been harassing her, to help run interference. If he tries to push it further, I think a good stock response is
"I'm not interested in a relationship with you. I am no longer interested in any sort of interaction with you. Do not contact me again."
If he pushes it further, or escalates (starts stalking, shows up at her place, email/phone bombing) contact the non emergency police line (or emergency, if he's standing outside her apartment right then) and ask for advice.
I will add two comments for future use.
First, if you turn down someone's romantic advances, it's a really bad idea to get pulled into discussing and defending your reasons. "I'm not interested in you that way" is *always* an acceptable and sufficient response. If you agree to discuss it, it tells them that it *is* up for discussion - they can change your mind through argument.
Second, one of the easiest ways to get involved in unpleasant or dangerous situations is to ignore or rationalize all the signs that things are off. If someone doesn't respect your right to say no to a romantic relationship, it doesn't *matter* whether they're malicious and doing it on purpose, or they're really a nice person under it all, or they are clueless socially and don't know any better, or they're horribly lonely, or you're the only person they will ever love. What really matters is that this is a person who does not acknowledge your right to say no, and regards what they want as much more important than what you want.
That doesn't mean you need to mace anyone who asks you out more than once. But it does mean you mentally flag that person as problematic, and carefully watch their behaviour and your own responses, so that you notice if things escalate or they don't back off, and respond appropriately.