There is absolutely no evidence that split personalities have anything to do with the split in the brain, biological things grow outward from a centre or a series of centres on a line. The brain ends up as two distinct parts for the same reason some people have cleft chins and relative symmetry of body.
How do you account for multiple personalities in your 'theory'?
Split personalities are a result of the brain fooling itself or locking off some traits from others, usually due to a traumatic event or memory suppression. Also, INDOCRINATION, forcing a belief on the person that they had not encouraged or wanted in anyway, starts a little brainwar as logic or previous knowledge conflict with the new paradigm.
This is why I believe a lot of Christians lose it when confronted with the flaws of their religion, and especially fundamentalists who incorporate RW Conspiracies and historical, political bullshit into their worldview. They go into panic because there's still a part of them that knows its all nonsense. That's why its much more common for them to use shouting and repetition as an arguing tactic, they're backed into a corner with their case having no substance and much formidable facts against it.
We all have a duality, certainly, but for most it's just for civility. To live with others you've got to do things and act like you know you're expected to when you really couldn't give a shit about. To fit in at home, with extended family and work related bullshit you'd just as soon walk from. For most of us "It's an eminence front, it's a put on", not another distinct personality.
Sometimes when they say someone's 'grown distant' it's usually a coping mechanism for too much shit going on, I've done this at times and seen many do it temporarily and heard people say "they've changed" but they haven't, it's a coping mechanism and it works better then blowing up and they're theirselves soon, even sooner if the bullshit stops. Trouble with fundies, the bullshit never stops.