My main character is pissed. His wife murdered, his son captured, the world he lived his whole life in destroyed, the company he trusted to keep himself and his family safe betrayed and used him for some stupid experiment. He then sees all kinds of horrors, flying limbs, mutated animals, brains, the smell, ghouls...
At the beginning it was about survival but after some in-game months combat became a piece of cake. Once afraid to fight and now it became a standard procedure, like riding a bike. Maybe even having fun?
Then after finding out his son is older than him and plays with lives and plays god, he says [censored] it and is in for some chaos. Freeing the synths so he can later kill the ones gone bad? Why the hell not?
So, he won't join the minutemen because he doesn't care about other people anymore. He joined and supported them at the start but as his heart turned colder, he just couldn't play the 'general' of some childish ideology.
He won't join the BoS because they're an army and that's not his kind of thing. He also can't trust their goal to save the technology. They're impressive yes, but too ordered and racist. And they surely be a tough enemy to face.
The institute stands for everything vault tec and other companies did and maybe they're much worse than all the pre-war companies combined. Technological progress at the cost of human experiments. Plus, he likes piper so no. And he hates that his son runs the place. He can't trust him, maybe they've made it all up and he's a synth or clone or whatever. Maybe they'll [censored] up the world a second time so no.
The railroad? They're rebels, weak people fighting the system for their own goal. A goal that simply seems right in their mind and a goal some people maybe think about but won't even lift their finger for it. To free the synths.With the railroad, my main character can lead the weakest faction to victory and cause a lot of chaos while doing so. It'll satisfy him more than siding with any other faction. Valentine became a good friend so he doesn't see synths as simple machines like codsworth. The minutemen want to give people good lives and that's something they need take care themselves for. Freeing slaves that can't do nothing for their situation seems more important to me.
Just thought I'd share. Sorry for typos.