He actually explains the how, why, and what...

The Institute needed a fresh human being who wasn't tainted by radiation and the wasteland. So they dug up things about the vaults and found out that there was a baby in Vault 111. The plan was to keep both parents alive, for future needs, but Kellog ended up having to kill your spouse in order to get Shaun. From there, they took Shaun in and raised him. Doing some experiments and eventually he grew to become the leader, raising in the ranks within the process. Kellog also became cyborg within his time dealing with the Institute. It all makes sense and is pretty fine honestly.

This is all much better story writing than Fallout 3 and New Vegas (at times). I am having a hard time which main story I like better between Fallout 4 and New Vegas myself.

Because the game deserves to be praised. It's one of Bethesda's best works honestly; however, like any game, it has flaws. Fallout 4's biggest flaw is honestly the dialogue system, which everyone pretty much agrees on and don't praise.