There's no evidence to lead you to believe he is a Serial Killer who enjoys slitting children's throats.
Sure there is. On many occasions he's lured children (a mere fraction of his age) into his va... TARDIS with the promise of fun and adventure, only to have them wind up dead not long thereafter. There's no reason to believe he doesn't like killing them himself. Heck, just look at how much more comfortable he is about being a violent psychopath (from outright running up to punch someone out, to committing the genocide of his own race, to vaporizing old men with missiles).
See, I can play that game of making-logic-up, too.
...but, there is evidence that he does consider himself married and is happy with River being his wife.
Consumating a marriage is a purely human concept. He's barely been shown to be comfortable kissing her since the marriage. Of course, he's also been implied to be a sex hound lately, too, but mostly with historical figures like Cleopatra far more than anything we've seen with River.
That said, I'm still not sure how it's okay to make things up if it suits your personal argument, but not when it's contrary to it. Until there's actual evidence suggesting it directly, it's just not true at all, no matter how many people agree with you. Argumentum ad populum