This is one of those instances were the mechanics and the themes of the game meet up, think they're going to have a wonderful time, then when they get to the bedroom it all gets awkward.
By the very nature of the furry community people have favorite species that they want to see more of and want to build decks around. So you'd think we'd make everything tribal [IE having a deck that's exclusively one species] viable. But if we did that then for gameplay purposes certain mechanics and fetishes would have to be tied to specific species simply because there wouldn't be enough room in each set otherwise. Then you'd get situations like "Well I like vore but I wish they'd print it on something other than snakes" or "Does every fox really have to be into bondage in this game?" or "Man I just love sadism but I can't stand badgers, Furoticon why must you taunt me so?"
We tried being vague about it in 1st Vanilla, with stuff like Feline Front, Canine Central, and Equine Exhibition, but that all got really confusing and wasn't well received. So the trade-off is every now and again certain species get some degree of tribal support. The Tanglebrook Six (Dragons, Otters, Wolves, Rats, Lions, and Shapeshifters) have the most tribal support because they were they're a nice mix of the most popular species. Certain others have cards to give a little bit of a bonus for being tribal (Constructs, Foxes, Horses, Jinvon, and Squirrels). Beyond that there's a few others that you can make decks out of, but probably won't be too good (Bears, Birds, Cats, Cheetahs, Cows, Dogs, Goats, Hyena, Mice, Rabbits, Raccoon, Skunk, Tiger, and technically Snake). Though technically any deck can benefit from being tribal thanks to [card]Kinship Studios[/card] and [card]Join the Team[/card].
Cats and dogs provide a bit of a pickle, as you've probably noticed, when it comes to this kind of typing. In other games they can just say "Cat" and call it a day, even if what's pictured is a lion or a tiger or a panther. The furry community (at least the feline parts of it) expect that distinction to be made. Canines have it a bit easier, since there's an easily understood difference between a dog and a wolf, and while there's different breeds of dog they're all technically the same species. Felines though, that's where things get tricky. There's just so many different species of a big cat. It could of been divided into Feline:whatever as it's typing, but that's just adding extra layers of complication that'd bog the game down. So felines lose a bit of mechanics support for the sake of distinction.
The other trouble comes from the fact that, mechanically the game is divided by gender, but that wouldn't make sense physiologically for certain species to be tied to a gender, and that would further divide the fans (see the fetish reason above). Special exceptions made to Otherkind, that gets all the invertebrates, and the Tanglebrook Six, which had to be divided up due to gameplay concessions.
With all that rambling said we're always adding in more tribal boosts where we can. We love hearing from players like you, it's how we can gauge what the players want see.