Sounds like he's been hurt repeatedly and learned to trust no one. He thinks he won't be harmed as long as he keeps everyone at a distance and never exposes a weakness. It's a common setup, quite relatable, actually.
Yeah, when you're a pessimist and see something that looks too good to be true, you can't help thinking 'what's the catch?'
You can tell he's thinking hard about it. He almost wants to give her a chance but he's sure it's a bad idea, because come on, who would suddenly take interest in him of all people without an ulterior motive? You know, that is a good question - what would she want from him - and she seems semi-hesitant to get closer herself, too.