El Mahdi
Muad'Dib of the Anauroch
It isn't the risk. It is the connection. I find I can read a dog much better than a cat...
Believe it or not, this has been scientifically documented as true, so it's not just your own feeling or belief. Dogs have, over the 100,000 years or so of domestication, learned how to read human faces (and vice-versa to a certain extent). It's a genetic thing that's passed along. Wolves do not have this ability, and even wolves that have been domesticated (as much as that is possible) are unable to learn this. Even in tests where foxes were specifically bred for non-agression, which resulted in very dog-like behavior and physical characteristics in just a few short generations - the Foxes didn't automatically gain the ability to read human faces. In dogs (and Humans), it's an ability gained through a 100,000 years of evolution.
Cats definitely do not have that ability. Your housecat (for those who have one), is only domesticated in the loosest definition of the word. They're used to people so are not scared of or aggressive toward them (for the most part). They may even go as far as to consider people (and sometimes other animals) as a part of their community, same as other cats of it's community (if it has/had one). But in most ways, that housecat is no different (other than lack of fear of man and size), than any wild feline - be it a Bobcat, Cougar, or Lion.
I've never been bitten by a dog I've owned (though other people's dogs are a different story), have been bitten or clawed by my own cats before.
I have, though never seriously. Dogs, like wolves, have much of the same "language" - a language that includes different kinds of bites (among many other things). Just as licking starts out as a puppy-communication asking for food, then morphs into asking for and showing affection; Dogs will lightly bite each others snouts to show playfullness and affection (among other things, such as aggression and domination). Sometimes they'll even do this with humans, though our faces aren't built for it and aren't as tough. I've also been bit by dogs I've owned when they were scared, though never hard enough to break the skin. Dogs have a language with which they communicate, but limited ways in which to do so - biting is one of those ways. Though it can be mitigated through training, it's impossible to eliminate entirely.