Body corporate won't let us own a pet in our own home

We purchased a unit title property a month ago. The contract said we must obtain consent from the Body Corporate (BC) committee to keep a pet. In this instance a cat. There are plenty of cats and dogs in the neighborhood. Our neighbours who moved in a month before us also have a cat that we love. But the BC told us in email they have rejected our application for adopting a cat as there are too many pets already and they are receiving complaints. They have said that from here on out no new owners can have pets and those who have pets already in some instance 2 even can keep them. This has really affected us as it is discriminatory against new owners. Besides not being able to have a pet like old owners do, it reduces the value of our property for resale as it isn't pet friendly to new owners. We pay the same rates to the BC yet have fewer privileges. Many people who move in with pets when they buy the home aren't being penalised like we are just because we followed the rules and asked for permission. We thought the permission was just so they could ensure the cat is neutered, dewormed etc. How can we pursue this? We are extremely disheartened. Any help would be appreciated.