Small dogs may not be able to kill you, but they can still bite in such a way as to permanently damage nerves/tendons/whatever.
One of the kids I used to play with when I was a kid was bitten badly on the ankle by our next door neighbor's nasty Dachshund. He got a permanent limp because of it.
Another guy I used to know several years ago got bitten badly on the hand by his own evil tempered poodle mix (nastiest dog I've ever known). He was a guitar player in a prominent band at the time and can't play anymore because of the damage.
A dog trainer I used to know has a giant horrible scar on her hand and wrist from an attack by her worst client - a poodle. She can't use her pinky and ring finger on that hand. Eventually, the dog bit one of their young kids badly, and they had it put to sleep.
I have a scar on the back/side of my neck from teasing one of the small neighborhood dogs when I was a kid (some kind of unknown mutt). Doctor told my parents that had it bitten me just an inch or so away were the carotid artery is I would likely have bled out and died. I still usually don't wear my hair up because of that scar though it has tremendously faded since, and the doctor did a hell of a job stitching me back up. Rather than being afraid of dogs after that I think it made me like them and respect them all the more because of the crushing guilt I felt about teasing it... I was evil pulling on it's tail though I don't know why I did.
The worst dog I think I've met yet was a Chihuahua about half the size of yours. Owned by a no-longer friend of my next door neighbor. It was still a puppy when she brought the beast over to show off. Being an accessory rather than a pet she carried it everywhere instead of letting it walk with its own legs, and it growled and snapped continually at everyone including her. It bit her at least a dozen times the few hours she was visiting until the last bite got her bad on the jaw that she had to go to the hospital and have stitches to put back the flap of skin and muscle it mostly tore off. After that she dropped it off at the pound and continued to complain what a horrible vicious dog it was though she got it as a puppy, and it was still not quite a year old when it ripped off part of her face. Stupid woman still doesn't believe the dog's attitude was entirely her own fault, and she's still furious at that dog for scaring her face.
There's a good reason why small dogs are often the most vicious growling, snapping and biting even their own owners beasts. Because the owners think it's somehow cute or that because the dog is small it can't hurt anyone, so they let them act like rabid shits. I know of very few small dogs that aren't allowed to bite when they please though some of them only do it in more extreme circumstances while most of them growl, snap or bite quite often.
They may not be able to kill an adult, but they can sure do some very serious damage and can kill babies and kids. Having a small dog is no excuse to not train it properly and keep it under physical control.
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I won't walk the neighborhood with my granddaughter anymore without an axe handle and pepper spray. Too many big dog owners with small fences. If one comes at her it is not going to get back off the ground.
