I like to imagine everyone, except Bruce,loves it when Damian brings in pets and animals to stay in animals but are bribed into secrecy by Bruce.They all love living in the zoo Wayne Manor has become and they each have their favourite animal.
Dick loves it when Damian brings in birds, especially Robins,as when he does gymnastics he pretends he's flying alongside them.
Jason loves it when rodents are adopted mainly because they absolutely terrify half the other residents in the Manor,Bruce included.
Cass loves it when Damian picks up Cats of the street as she and the cats usually sneak around and scare anyone and everyone.
Tim doesn't necessarily have a favourite animal but he loved it when Damian snuck Detective Chimp into the Manor when he was in horrific dept and the two would trade conspiracy theories and solve unsolvable cases. Bruce is constantly terrified for his job if those two worked together.
Stephanie is a die hard dog lover and easily succumbs to any begs for treats and frequently walks Ace,Titus and all the other dogs.
Duke is amazed by reptiles and watching them slither. He's always first to search when Damian's lost a snake or beaded dragon.
Babs loves the insects and helped Damian when he adopted a beehive it was the day she first saw the bees she truly adopted the title Queen B.
Even Alfred has a favourite much to the dismay of Bruce. He adores horses and taught every batkid how to ride them and groom them. He also has an English Bulldog who he named Elizabeth or Lizzie.
Bruce loves Ace. Ace is his favourite child.