...did she forget about the whole 'no dating' rule in their home? and even if there wasn't such a rule, it's not like they're a couple in any kind of formalized sense, if anything it'd be presumptuous of him to just kiss her out of the blue, especially when she's been far from cheerful over the course of the date. it just seems like she's jealous that he's talking about the particulars of their housemates rather than focusing his full attention on her.
I get wanting validation from the guy you're in love with, but so far on this date he's just been matching her energy. the rest is him clearly not wanting to intrude or impose himself upon her, like when he didn't want to interrupt her when she was studying the painting.