Ontological Paradox resolved

Two friends A and B are casually talking and time travel enters the conversation:

...
A: Do you believe in time travel?
B: Are you serious? Of course!
A: You mean of course not?
B: No! I mean of course I do!
A: (Surprised) Are you serious? You've never told me that. How come?
B: Not only I believe in it. I do it all the time!
A: (Even more surprised) What do you mean? Really?
B: Sure! Just yesterday I traveled back to the Golden Age of Pericles in Athens, for a while.
A: (Very excited) You really mean that? That's incredible! What did you see, did you see the Parthenon being built?
B: No, I'm afraid not.
A: Did you see Pericles speaking in agora?
B: No, I'm afraid not.
A: Did you see Phidias sculpting the golden statue of goddess Athena?
B: Unfortunately I didn't see that either...
A: What did you see then?
B: Mmm, to be entirely honest, I couldn't see anything at all...
A: (Deeply disappointed) Oh no, what a pity! Why, what happened, something went wrong with your time machine?
B: No, everything was ok, exactly as it was at the time but, you see, I couldn't see anything myself because, back then, I hadn't been born!