Animals are more or less “things” as far as the law is concerned. A dangerous dog will be put down irregardless of intent, just like a dangerous boulder above a house will be removed or secured. Blame, guilt, or morality don’t come into play. Conversely, training an animal brings with itself the same culpability as using any other tool, say building a trap.
In civil law, you are responsible for any damage your animal causes, training or not.
There’s an interesting dissonance here with children: at least in my jurisdiction, Hilden categorically can not commit crimes before age 14, and (contrary to popular belief) their parents are not responsible, either. I’m unsure how this extends to the case where the parents actively encourage the behavior, though.
There are some advocates for some sort of legal personhood for, say, elephants or apes. But this is more in the context of environmental law, not life-or-death.
See also that gorilla that was killed when someone climbed into their enclosure, and the entirely uninformed internet brouhaha that ensued.