Aside from the "cuteness factor", I think a large part of it has to do with the fact that canines, foxes, felines, and dragons even, are the animals people are most familiar with and know the most about. They've been a major part of folklore, always recognizable, and generally are much easier to match with a personality because of all that.
It's easy to think of wolves and think "pack mentality, strong, etc." It's easy to think of foxes and think "cunning, resourceful, etc." It's easy to think of cats and think "independent, playful, etc." But it's not so easy to think of what a squid thinks and acts like. It's difficult for people to know where to begin when describing the personality of an ibex or a tarsier. There's millions of fantastic creatures and species, but most people just aren't familiar enough with the animals to even know anything about them sometimes, let alone feel a connection with them.
So... combine all that with the fact that "everyone else is doing it", and there you go.
