I thought about Father being a psychopath or sociopath. It's plausible and it fits with almost everything we know about him. The only thing I don't then understand is why he didn't leave his remaining parent to die in the Vault. Or, if he did have an inkling of the feats of which they might be capable, why he didn't just have them killed to eliminate a potential threat. I don't see why a psychopath would care enough to save them at all. Normally, the assumption could be that there was some sort of Norman Bates psycho-sixual obsession to drive the decision. In this case though, Sean never knew his parents, so they make an unlikely target for obsession.
That said, it's as good an explanation as most I've come across. Personally, I think I'm tending towards the player-as-synth theory, but there's nothing in-game to support that.
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Of course, there is the question of why the player's DNA was special. We're told the Institute needed uncontaminated DNA for the Gen 3s, but there was a full vault of the stuff. All they needed to do was crack open a coffin at random an take a few cell scrapings. Or thaw out Old Man Neuberg and explain that he could live in relative luxury in exchange for his co-operation or he could beg for water in an irradiated hell. I bet there'd have been plenty of volunteers.
If the player's DNA had some particular mutation to it then that would explain Kellogg's otherwise needless brutality and PsychoShawn's desire to test his parent. But I suspect that most players would be uncomfortable with the idea of the PC as being some sort of latent ubermensch from the word go.
All in all, I think I prefer my initial assessment: It makes no sense at all.