I don't really think that the majority of furry characters being canines has got anything to do with therians, though.
A therian doesn't choose his species, he simply is. It's just in their behaviour, psychology, or "soul" if you want to go that route. He's just born, and (in my case, for example) just slowly begins to realise that he's almost speakingly dog-like in his psychology, or (in other cases I've heard of) comes to this knowledge trough dreams or visions.
And, as far as I've seen in my own eyes, yet, canines aren't a solid majority in therian numbers, as well, but, keep in mind that I may be wrong there.
As concerned to just regulair furries.
The reason why canines are soo populair, may be that there has always been a relationship of some sort between humans and canines.
At an already quite an early age of human development, they figured out that wolves could be friendly, and could help them with various things, like hunting, and guarding one's properties. Later on, this became a seperate species, I.E, the domestic dog.
Nowadays, dogs are simply everywhere. Any individuals family member undoubtedly has one, or has had one, or they may have even had one himself. And even if they didn't, with the number of people owning a canine as a pet, or for work (police, and stuff) it's undoubtable that they'll, at multiple points in time, come into contact with dogs.
This contact may sometimes be of a positive experience, like a friendly dog, randomly coming upto you, and making your day better, and sometimes as a negative one, like a scary, rabid dog, running upto you and attacking you. And sometimes, this good, and the bad alike, may come from the very same dog.
Thus, the relationship between humans and dogs hasn't always been spotless. Sometimes it works out, and sometimes it doesn't. And, I personally believe that these mixed feelings even further strenghten the influence that canines have on the human culture.
Skip forward a few thousand years, if not more, and canines are everywhere...
They're in people's homes, they roam the streets as strays, they wolves are in the zoo, as well as in the wild. And, they're in art too. People write books involving them, or even starring them, they draw comics or make animated movies.
Just think about how many examples of canines and art can you come up with? Probably a lot...
And, eventually, furries became a thing and, well, canines gotten their influence in that too.
The first furries were probably inspired by other canines/canine characters in books/comics/animated movies, and the ones to follow then probably just followed the trend.
And, then we're here...
And, what about cats? I hear you ask...
Sure, a cat may occasionally bite someone, or be his friend, but never scars someone for life with a vicious attack, or neither commonly becomes such a beloved companion that their passing hurls someone into depression.
Felines simply aren't as strong as canines. They simply haven't been involved that much in actual human affairs, and haven't caused us such strong emotions.
Hence, they're less populair.
Questions? c: