I have no idea why some people do that. I think it's a pathetic attempt to get you to pursue them and beg for their attention. Maybe they're trying to gain the upper hand instead of being mature and rational? Or just playing you to get validation for their own self-image issues. Honestly, who knows.

I would say act accordingly and with self respect. I had a coworker do the exact same thing to me many years ago. I decided to not play that stupid game and date someone else. She absolutely lost her shit and I couldn't care less. Their loss.