Why was Dan happy about delivering the baby?

Dan was thrilled about delivering his first post-Day baby because it meant that the human race would survive the tragedy.

"Yes. But that's not what was wonderful." Dan's smile disappeared. "You see, this was the first live baby, full term. I had two other pregnancies that ended prematurely. Nature's way of protecting the race, I think, although you can't reach any statistical conclusion on the basis of three pregnancies. Anyway, now we know that there's going to be a human race, don't we?"