Why positive only training?

I'd like to ask a question about positive training methods that I realize will be a little controversial, just to be clear I am not a dog trainer, just an average owner interested in learning.

My question is this: why use only the positive in absence of the negative?

I understand that a positive association makes the behaviour more likely to occur again but shouldnt the inverse also be true, a negative association makes the behaviour less likely to occur again? Essentially, consequence cuts both ways... we teach our children using this idea, why not dogs? Its true that the human psyche is different from a dogs but dog-dog communication is almost exclusively negative (you will not see a dog give another dog a treat, but you might see one snap at another). Also why is dominance theory so denigrated, dogs aren't wolves but they do have pack hierarchy. Shouldnt we be trying to communicate with dogs in a "language" that is most natural to them?