I wanted to breed my pet, Rain (my starter pet) but I can't breed her. I have no idea why. I feel like if the answer was a snake, I would have done been bitten on the nose by now.

Your starter pet is an Adolescent. It will become an Adult after 648 hours.

Link: https://www.sylestia.com/forums/?thread=103524&page=1#2 Author: T1g3r Time Posted: 8/18/2022 at 5:00 PM Your starter pet is an Adolescent. It will become an Adult after 648 hours.

Oh! Okay, thank you!

Pets made via the generator (including starters) start life at 216 Maturity Hours.
Maturity hours are different from 'time a pet has existed', and determine how old a pet is: 0-72, eggling, 72-216, hatchling, 216-648, adolescent, 648+, adult
(that is, from newly bred egg to adulthood, if no methods of speeding growth occur: 3 days as eggling, 6 days as hatchling, 18 days as adolescent, hitting adulthood at 27 days. Starters and generator pets skip the first two and only have the 18 days of adolescence)

With generator-made pets and pets that have been genetically tested (people offer testing services for free in the Groups, Guilds, Clubs, and Services fourm), you can see their exact maturity hours age in their profile.
This is Rain's:
Birthday: 08-18-2022 03:46:37AM
Age: 15 Hours
Maturity: Adolescent (232/648) <this bit right here is the relevant bit, showing she has 416 mh (bit over 17 days) of adolescence to go until she hits adulthood.

In untested pets you can only see the stage of life, not the exact mh age.