Because he's a drunk and it's all about him and his needs. Do not for one instance think this woman is any smarter, prettier, sexier or skinnier. It has NOTHING to do with any of that crap. Cheaters are insecure self loathers...it's all about their own worthless ego gratification. In all likelihood, she is probably more controllable than you...she is likely less of an emotional or ego threat.
He probably feels better about himself with her cuz in some way he feels superior to her for whatever reason.