The Proof is in: Extinction is Dead

A certain faction of the dog training community honestly and firmly believes that you can train a dog using two things: one is treats, praise and toys.  And the other one is ignoring certain behaviors.
By ignoring them, they assert, your dog will not be rewarded, and hence he will cease to engage in that behavior.  This, then, is called ‘extinction’
The fallacy to the argument is this: sometimes rewards come from somewhere other than us.  Dog behavior just cannot be distilled down to only what we are giving our pal, even if we wish it could.  The fly in the ointment even has a name: intrinsic rewards.  These are the psychological rewards, the ones that we give ourselves.  In humans, it can be that good feeling you get when you work out, keep a promise, or give to charity.  Dogs have the benefit of intrinsic rewards as well.
Consider: the desire to mate has nothing to do with us.  The desire for a dog to mother her babies includes no treats.   Even rolling in something dead is devoid of our praise.  These behaviors do not need something from us to reinforce the behavior: dogs do these things because they derive some satisfaction from the very act. Instinctive and bred-in behaviors fit this category as well.  These dogs were bred to do a job well, and they enjoy the work they do.  Even if our dog doesn’t need to use his prey drive to stay fed, he will still kill small animals.
We can only cause ‘extinction’ in behaviors where the reward comes DIRECTLY from us.  For instance, if we have a toy our dog wants, and he is staring at us waiting, but we fail to throw it, eventually the dog will get bored and walk away.  The next time, he might give up faster.  Eventually, he won’t believe we will throw the toy at all, so he won’t bother to wait.  Again: we had complete control of the ‘reward’ (the toy), and we did not give that to our dog.  It would be a slower process than if we told our dog ‘no’ in the first place, but it would eventually create the same reaction in our dog.
But that only describes a very small subset of things our dogs want.  You cannot use extinction to stop your dog from barking at other dogs or the mailman.  You cannot use extinction to teach your dog not to jump.  Any behavior for which we do not hold the reward, that is in some way enjoyable for our dog, will not go ‘extinct’, no matter how much we ignore the behavior.
And without a correction of some sort (even just a disappointed frown), your dog will have no way of knowing you don’t like the behavior.  Because we aren’t communicating clearly with our dog (silence is not communication here), he is left in the dark, having a grand time jumping on our guests.
Why this theory started 
It helps with many of these odd ideas if we consider ‘Purely Positive’ as an over-reaction from a certain group of people.  They wanted to get away from harsh corrections and a host of things they believe the Dominance trainers were doing that was harming dogs.
Sadly, they went much too far in the other direction.  Instead of correcting misbehavior, they insist, we just have to ignore it.  They do not feel that any sort of correction is necessary in dog training.
It is misguided and scientifically inaccurate.  Worse, I think it puts both people and dogs in very real jeopardy, and unless this theory is put to rest, we can look forward to a future where our dogs are not allowed into any social situation.
Of interest: while looking for information through Google, the first three items on the list were ALL related to why ‘extinction’ is a non-working theory.  Perhaps the tide is finally turning!