Okay, first, 16, 17 and 18 year olds are biologically sexually mature human beings, so in the psychological sense--erotic attraction to pre-pubsecent children--Foley shows no evidence of pedophilia.
Second, under the laws of DC, 16 is age of consent, so legally, having the hots for Congressional Pages is not pedophila.
Why resign? Loyalty to party, an estimation that being outed as a homosexual who was into teenagers would ruin his election chances. Because he really is a drunk and doesn't recall what actually happened three years ago.
If Edmunds goaded him into exchanging lewd IM's, then the incident becomes akin to entrapment.
Honestly, if you are single (or imagine yourself--may God forbid it--divorced or widowed), and an attractive young person on the cusp of adulthood and already the age of consent wherever you are (if you're in a state where it's 18, imagine a great job has moved you to Kansas or DC, where it's 16) comes on to you, mightn't you act a bit giddy and goofy, do stupid things?
Homosexual recruiter.