I see this in quite a different way to others.
A person who genuinely had realised he wasn't ready for a relationship would recognise that the other party may well not want a friendship, and would respect that.
They would also not attempt to impose controlling terms on that other person. At the very least, as well as MH problems, he is also selfish.
But he's following a well-known toxic script - the blowing hot and cold, keeping the OP confused. Not accepting her decision to end things completely.
This was a pure push for control, and for putting the OP on the back-burner when he thought he had her hooked - well done OP for not accepting his breadcrumbs.
Dana Morningstar often says that confusion is a first warning sign of an abuser - because we try to find ways to explain their behaviour that do not involve the real underlying reason - a bid for control and for making their target feel 'less than'.
Even if it does turn out that this man is 'only' a timid woodland creature who has to be tempted and nurtured whilst simultaneously not scared off - I presume that is not the sort of partner you would want, OP. His actions on the date are not him, they were him wearing hid 'date mask'. This is him.
There will be nicer men out there.
I'd bet he's still on the dating site, despite having 'realised' he is not ready. He'll find some poor unboundaried woman who will put up with his crap and he will lead her a merry dance for years. Be glad it isn't you, OP.