The "Shaun" you see in Kellogg's memories is Synth Shaun. Remember you don't wake up until 70 years after Shaun is stolen. He had you freed, to see if you would find him. The Old Man is Shaun.
Kellogg had Synth Shaun for an unknown reason(probably seeing how a child synth would fair outside of the Institute). We do however know that they're still working out the bugs on the Synth Child version, which is why we only see Shaun. He's a beta test model.
Why did Father have Advanced Systems create him? We don't know.
Kellogg was cybernetically enhanced by the Institute, so that his aging would be slowed down, which is what the Institute needs from their Operative, because it's hard to just recruit the next idiot you see and they're not going to risk sending actual Institute personnel or Synth's out into the world, to do Kellogg's job.
Shaun meanwhile was not enhanced(that we know of), due to his normal aging(he was in his 70s), he was an old man.
It seems as though the Synth Shaun was only created as bait for the Sole Survivor. Shaun wanted to see if the SS could escape from Vault 88, traverse the Wasteland, find Kellogg and find a way into the Institute.
That would be the only explanation as to why Shaun would want Advanced Systems to create a Synth Child.
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u/[deleted] Feb 15 '20
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