Support. Being able to keep up with families is something a lot of people tend to enjoy. I like knowing the children and grandchildren, so on and so forth. This can also be very handy to prevent inbreeding, if the site has implemented the possibility of negative effects from such.
Edit:
Guess what, if you go to a creature's page and look on the right-hand side, there's a 'Pedigree' button that shows the lineage of the creature. So this has already been implimented. Silly us.
Edit 2:
Not sure why, but the parents pedigrees do not list the offspring. This may change once the baby grows to adult. I'll touch back later with the result, if no one else confirms this. As of now, if you click an offspring, the pedigree information does show up.
"You know what the issue is with this world? Everyone wants a magical solution for their problem, and everyone refuses to believe in magic."
- Jefferson/The Mad Hatter, Once Upon a Time