Why would a guy become friends with a woman he knows likes him?

It's because he doesn't have interest in you or his mutual friend.
Also about starting the friendship, he just wants to establish a friendship with you, not for anything more than that.

It's probably some sort of egotistical confidence boast. It makes him feel in control so he uses it as a power trip, and he also might want to keep friends with you so he has a backup plan if the next girl he dates goes south. He doesn't sound like a great guy, I'd say get over him and find someone better.

idk it sorta sounds like he's comfortable with you because you're OK being his friend. perhaps that's what he needs right now. who knows. I personally know where I am in life right now all I want is a friendship and nothing more. sometimes there are personal things going on in our lives that don't make us emotionally available to have anything more than friendships with those around us. if you can honestly handle being just his friend than who knows what could happen? you could actually become a very good friend of his who he may be able to talk to about what's going on in life. take care and good luck on this one. its ultimately up to you with what you want and do not want in life right now. I hope this helps.