Went to search some high stat ryori males to diversify my brood with again today clicked on a pet, went to breed and it said "one or both of these pets don't exist". realised it had 0 hunger, fed it, still nothing, realised I hadn't selected my female. Went to the drop down and it's blank, no stable options nothing even on multiple reloads, new tabs. Try a different male same thing.

I took a look in your stable to see if I could spot the issue, and it looks like your problem is twofold:

-three of your female ryoris are only adolescents. Pets cannot breed until they are adults
-the rest of your female ryoris are still recovering from being bred. Females of fabled species, like ryoris, can only breed once every seven days, whereas non-fabled females can breed every three days.

As all of your female ryoris are either recovering, or not old enough to breed, none will show up on the drop down for breeding with males owned by others.

Sorry, I have lingering issues from a brain injury and mistook a newly adult ryori for female when they are male >_< I checked things a few times and just got the names confused I guess. So sorry for the wasted time.