spoiler warning, if you haven't found them yet ^^

so why didn't they do it?

They are so happy to see me, when I arrive there... and their leader turns out to be my son and wants me to work with them.

And I keep having this question in my head that keeps me from siding with them. Why didn't they try to contact me?

'Father' seem to have known that I was still in the vault, still alive. He could've easily sent a courser there to free me, when he was already a leader of the whole faction.

Do I miss something here? Or is it just a flaw, in the way the story is told?

No, Shaun will see / test you if youre able to survive and find the Institute by yourself. Institute needs a strong person.... just follow the Institute questlines, but be aware of the "point of no return" quest stage. If you want to be on friendly term and no hurry to finish MQ, begin to do the radiant quests. There are 5 of these, just follow the colour marking on the floor.

Cheers,

-Klevs

And that is why I blew them up the first time around... "Father"... he leaves his own mother on ice for 60 years, and then, like an after thought, he frees you, just to see if you would even survive the Commonwealth. My first character said, "Is that all I am to you? A Science Experiment?" Oh she was hot!

So yea, there are many discussions around these boards about the various factions. Some people are for and many are against the Institute.

I also would like to know WHAT Shaun was actually thinking here and why they had to kill ALL the people in vault 111.

Imo, they need a DNA from a youngster, a DNA that is not polluted. They only need Shauns. They did not kill you, because they suppose needed a kind of "backup". When Shaun took over, he decided that you cannot be killed, but rather see if you are able to survive and find the Institute. See how much you miss you son.

Cheers,

-Klevs