Many things are said about the Great Pyrenean Mountain dog. Some make sense. Others are so many old wives' tales. You may want to think carefully about the breed's purpose in life before you buy into some of them. You also must be careful about what kind of dog is being discussed. A mixed breed dog will certainly not behave the same as a pure bred dog since other breeds' characteristics will be mixed in and diluted the true behavioural instincts.
Some say …
'A dog doesn't need to registered to be a good dog.' This is true, but it cannot be called a Pyrenean. If it is not registered, you do not know if it is a true Pyr nor if he will show the breed behavioural characteristics that you desire.
'Pyrs are stubborn.' Well, no. A Pyr needs to be trained according to the type of dog he is. A Pyr needs two things to be happy; a friend and a job. There must be a relationship with the person he chooses as 'his human'. He needs a friend. As a working dog, he needs a job; he needs to have something or someone to guard. If he doesn't have these, he will be unhappy. He may chew up your slippers, your shoes or your couch to show you this.
The golden rule is that the fault is with the human, not the dog. Take a good look at how you treat or train him. Go to a trainer who knows Pyrs, ot just any trainer who tells you that he or she can do it.
There are many good trainers that can't work with Pyrs. There is no lost cause with a Pyr. You do have to decide how much and what kind of time and energy you are willing to invest in your dog.