Paolo Bacigalupi explored the other side of that coin in his short story Pop Squad (also made into an episode of Love, Death, and Robots). If you live forever, what's the point of having offspring?
It also touches on a theme of The Hydrogen Sonata (and elsewhere in the Culture series): with unlimited time to practice, how far will one go to perfect one's art (music in this case)?
I think it's related to reproduction - immortality would mean you're competing against your offspring for resources.