I see two likely scenarios:
#1 - Obama just lied because thats what he does. #2 - Cause the "girlfriend" was a dude. While I see either as a possibility, I figure it is probably #1.
Why he needs to lie about old girlfriends is subject to conjecture, but it's clear he lied:
-- Either he lied when he represented his book as an autobiography (i.e., a factual account that does not allow for "composite" characters); or,
-- He lied about having a girlfriend -- at least this girlfriend.
The guy is unbelievable. You literally cannot believe anything he says. (What a way to go through life!)