Is there any way to set a new active pet? I apparently can't breed my active pet so I'm trying to switch it out. Thanks!

To remove a pet from your party, go in the party manager and seledt the red - besside the picture of your pet. Tho you should be able to breed any adult pets that were not made unfertil, them being in your party dosn't change anything, make sure they are not adolescents. ^-^

Your active pet is just whichever one is in slot 1 of your party.
Assuming the pet you cannot breed is your starter Kori, this is because she is Adolescent.
Pets cannot breed until they are adults.

In genetically tested pets and pets made via the generator, you can see exactly how long it will take for them to grow by looking at their info:
Birthday: 11-06-2019 10:33:23AM
Age: 8 Days
Maturity: Adolescent (410/648) < this one.

On untested pets, you can still see if it says if the pet is Adolescent or Adult, but the numbers that show up after testing (or automatically on the generated ones) represent the pets 'maturity hours'

In this case, as of us writing this, Kori is 410 mh old. All pets made via the generator (including starters) start at 216 hours (the very start of Adolescence for a sylesti), and 648 is the age pets become adults.
so 648 - 410 = 238,
238 / 24 = 9.9 days until she reaches adulthood