Whether you use punishment or reward, the end result is always a strengthening of the targeted behavior. To very easily understand this concept, lets look at the definition of reinforcement (as given by Google):
re·in·force·ment
ˌrēinˈfôrsmənt/
noun
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the action or process of reinforcing or strengthening.
synonyms: augmentation, increase, supplementing, boosting, topping up "reinforcement of the bomber force"-
the process of encouraging or establishing a belief or pattern of behavior, especially by encouragement or reward.
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And thanks to my highschool English teacher, Mr. Deblois, I can see that the different parts of this word (re-in-force) literally translate to: "put force back in." So by reinforcing a behavior, you can only add strength to it. It may seem that if you punish a dog for getting into the trash, peeing in the house, or barking at a stranger, the behavior is reduced. However, what you have actually done is created an emotional charge around that very behavior. A charge that may not come out when you are around--because yes, the dog has "learned" not to do these things in your presence--but this now deep-seated stress around the behavior will eventually have to come to the surface.
And this is how most of us really stress our dogs out: we give them total freedom in the house from day one, they explore and get into things, they chew our valuables, and then we yell, scold, and correct them for very natural behaviors. Now the dog is deeply confused and cannot make a connection with his owner. Eventually he has to vent this stress, and that's where we get behavioral issues that make life difficult for everyone.
Deep stress held by the dog cannot be undone by "positive reinforcement." It's impossible to click away aggression. What we must do is gradually trigger the dog to release this held-back stress, and then smooth it out into a pleasant and happy experience in which he comes into alignment with his owner.
Clarification: What I'm calling negative reinforcement is technically termed "positive punishment" in the R+ community. Which to me is confusing as all hell. There's nothing positive about positive punishment, and it has been shown to be ineffective at the least and damaging at the worst. The R+ camp also defines negative reinforcement as the removal of a positive stimulus. Which I find to be equally ineffective as a practice, and also the language is equally confusing.
Anyhow, if you are used to the R+ quadrant of negative/positive punishment/reinforcement, then I just wanted to clear up the way I'm using those terms. So in essence, what I'm saying is: "positive punishment" simply reinforces the unwanted behavior, and that's negative!