Way to use spoiler tags, fuckers.
Spoiler Alert, click show to read:
As should be obvious, Jack's Ryan's biological son with Jasmine Jolyne. Ryan figures this out right before you meet him, and alludes to it, and is trying to make a point/free Jack, or prove to himself that his own son wouldn't be a slave. "A man chooses, a slave obeys!"
Playing through a second time, I found it a bit more obvious, knowing what I already did.
Note that Jack is only 2-3 years old when you play Bioshock