I honestly dont know when this myth started. I know lots of followers of a certain TV celeb seem to strongly believe he is the last chance for many aggressive dogs because other trainers would just have the dogs put to sleep.
This is as far from the truth as is possible. But before I go into that lets look at the fact that yes, many dogs are put to sleep
In the world today we have more dogs than we have homes for and so it is a sad fact that in some rescues some people have to make the difficult decision to put dogs to sleep.
That is not a failing of the rescues - and it has nothing to do with any trainers - positive or otherwise. The blame there is firmly on the heads of the people producing too many dogs.
Yes often it will be aggressive dogs or dogs of a certain type who are put to sleep, there are two reasons for this, it is harder to find good homes for these dogs, there are plenty of homes for small fluffy puppies so it makes sense when you have to free up space to go for the dogs that are unlikely to find a home anyway. Also if a dog has bitten in the past many re-homing centres have policies of not rehoming these dogs incase they bite again, not only would the people in the centre feel responsible they also may end up being sued and that will have a cost impact on how many dogs they can help in the future.
Some trainers may refuse to work with aggressive dogs, that does not mean they are saying the dogs need to be put to sleep, just that they either do not have the experience to work with this type of dog or their insurance does not cover them for this type of work.
That is fair enough, there are specialists in every walk of life, you dont go to a pet dog trainer to teach your dog to be an obedience champ, dont expect all dog trainers to be aggression specialists.
Referring you to someone else is NOT saying the dog needs put to sleep.
For a behavioural issue you need a behaviourist (try the APBC in the UK, these people have to be qualified to a high level with lots of experience in the field as well - remember anyone can call themselves a behaviourist but not everyone has any qualifications in the subject)
A GOOD behaviourist wont even see you till you have seen a vet to rule out any medical issues.
So do behaviourists tell people to get their dogs PTS?
Lets think about this - someone whos job is to help dogs with behavioural issues telling people to put the dogs to sleep - do you think these people would actually be in a job long if they killed off all their clients?
When talking about options they may well mention it as an option - IF the owners dont feel they are willing or able to do the work required to help their dog. Even using punishment methods to 'fix' a dog takes time, the TV celeb often takes 'difficult' cases away with him to work with them over weeks or even months.
Issues like seen on TV shows are bread and butter to good positive behaviourists, you dont see thousands of films of them helping because it is actually very dull to watch, no man v beast fight, the dogs are kept calm and taught how to not only act calm but to BE calm around the thing that they used to be aggressive about.
If you still doubt positive trainers help aggressive dogs then have a look at all the literature that is out there to help people with problem dogs - I will link a few below
Click to calm
Stress in dogs
Thousands of positive dog owners quietly rescue and help difficult dogs all over the world, just get chatting to people ringside at an agility show or have a look at the many forums and facebook pages for positive training and you will see what an amazing supportive community there is for people helping others with difficult dogs