When you see that exception, the first thing to do is to follow its advice.
VeryHelpfulExceptionMessage wrote:
org.hibernate.PropertyAccessException: exception setting property value with CGLIB (set hibernate.cglib.use_reflection_optimizer=false for more info) setter of com.test.RescueCenter.setPets
I'm a very helpful person, so I'll (very helpfully, IMHO ;) point out the very helpful part of that message:
set hibernate.cglib.use_reflection_optimizer=false for more info
Actually, I'm not sure how it gets that far, seeing as you've got a <list> without a <list-index>. I didn't know that that was possible. Chances are, the exception is a side effect of the bad mapping.