The unique domain that I would otherwise have to associate myself with. "gmail" is so ubiquitous that it just doesn't mean anything anymore. It's just... the protocol.
Tell someone that your email is "alice@alice.website" and even _that_ is saying something significant about yourself that you may not want to say.
A big aspect of appearing "cool" is not letting on that you care so much. Social networks and messaging systems should allow people to be "cool" if they want to be.