I answered this in another thread, but I'll go ahead and answer it for you here too.
In short, there is never any explanation given. During my run in FO4 where I sided with the Railroad, I ended up working with the Institute. I searched the entire place, read all the terminals, especially the ones in the Synth creation/rehabilitation labs, and there was nothing. Absolutely nothing.
There's 2 quests in the game involving people the Institute kidnapped. The first is a farm called Warwickstead. The father there was a drunk alchoholic, and the Institute kidnapped him and replaced him with a hard-working synth duplicate who also planted modified Institute crops which are supposed to grow a lot faster. During the quest, you have to take him new crop seeds to plant. During the whole quest, you cannot even once ask the scientist why the Institute is kidnapping people in the first place. You can't even betray the Institute during the whole quest. You find out one of the farmhands knows the father is a synth. Rather than being able to help the farmhand out and expose the father, your only options are pro-Institute. They are: Kill the farmhand before he can expose the father, or blackmail the farmhand into keeping the whole thing a secret.
The 2nd quest involving synth kidnapping is the Mayor of Diamond City. He's a synth. Once again, you cannot ask the scientists why they kidnap people from the Commonwealth, nor can you really find out any reasoning for it. He just gives you some papers, tells you to go see the Mayor and deliver the papers to him. That's it. No questioning, no looking deeper into it, nada.
It's the same for the Super Mutants really. Why the fuck are the Institute creating an army of Super Mutants over the course of 10 years? Literally the only explanation we get is in a holotape by Virgil, wherein he says "I don't know why Father keeps forcing us to make these abominations! I've asked him multiple times to shut down the project but he refuses! He says to keep going!" So yeah, they made Super Mutants, for 10 fucking years, simply because "Father wills it". And that's the only explanation we're given.