I think that the first things we asked before beginning Bojack Horseman was, "Why an anthropomorphic horse?"... well, yeah, after watching many episodes, that questions sounds less important. I know that there is no profound reason of why the characters are like that; but now that I'm waiting for another season of Bojack, why not trying to formulate a hypothesis about this strange animal/human society!
First. Why a horse? I like the way in which someone can relate with a character and find a meaning behind them (even when none of these have a meaning in life). I think that Bojack is more than a main character, but the reason why we are introduced to this absurd world (search the word "absurdism"); he is an allegory of the phrase "working like a horse", we know that Bojack is the opposite to that, so that makes it something funny. Bojack is the main character of the story, because he is the only one that sees how absurd that world is −he is the only one that noticed that Vincent Adultman was a child!
Second. Society with animals? Maybe it's a way of describing how different opinions and ideas looks when gathering in a same place. The jokes that they make through all the serie −Dogs putting their head out of the car's window, the birds in the electricity cables, etc. −are all stereotypes of how we see animals, but if you have noticed, they are all absurd stereotypes to identify animals. That's how racism looks like in other adult shows, something absurd that people laugh of.
Third. F*cked up biology! The capacity that these creatures have to reproduce is so weird, but knowing the way in which they see relationships between other animals is like how we see having relationships between people of different races, social classes or traditions, as we well see in the episode in which Princess Caroline meet the family of Ralph Stilton. We can simply call it "the uneven yoke".
When two different species (at least in this show) have a baby, the result depends of the dominant gene; there's no character that looks like a mutation of their parents. As in the case of Hollyhock, she looks more like her real father. When the baby is an "accident" or the son of a broken marriage, the baby carries the guilt of being similar to one of his fathers; unfortunately, we can witness this events in real life.
Finally, an idea that jumped in my head while writing about the biology thing... there are many human characters in the show, but have you ever seen an ape? (Not the Jogging Baboon, he is a monkey, even when he has no tail.)
Hope you like this hypothesis; maybe if you think the same, it can becomes a theory :D