It's kind of a multi-part revelation.
In one audio diary, a technician talks about how the bathyspheres are coded to Ryan's genetic signature, specifically to avoid anyone moving about as the like without access. It's further stated that the "genetic coding" isn't really exact and will work for anyone who's closely related.
In a few various audio diaries/moments with ghosts, we see that Ryan had a child with a whore, and that Fontaine took that child, to make you.
Finally, there's a diary from Suchong that says:
"Initial Deployment, Vita Chamber/Client Ryan Industries Stage one is complete. Sinclair and Alexander tried to explain the science to me, but Suchong does not believe them. They keep saying plasmid reconstruction this and quantum entanglement that, and then poof, dead people come back to life. Bullshit! Of course, Ryan will only allow it to be tunes to his genetic frequencies for the testing..."
Put it all together and you have your story. Too many people skip this stuff and then compain that it doesn't make sense.
- J