Real life advice:
He should have said no.
It will only create insecurities for his girlfriend and makes everything a bit more toxic.
He doesn't need to cut ties if she stops flirting or trying to seduce him, but he has to if she press on.
Manga life comment:
Eh, who cares, more drama incoming to make the story longer, or simply an author who can't make a rival not love about the MC