DAE find themselves at the mercy of the animal distribution system?

Does anyone else find themselves always acquiring new animals randomly as if you were chosen by them? It has happened more than 5 times in my life, and I don't know what to do about it. I have so many animals. It's going to keep happening. I have been chosen by the cat distribution system 3 times, dog distribution system once, guinea pig distribution system 4 times. I feel another dog is in my future.