I disagree. I got my dog from a rescue shelter when he was, the vet estimated, eight years old. He was a street dog for at least some of the time before his rescue. You would think that this would make him aggressive, and unable to accept training.
Since then, he became a certified therapy dog, and we have been volunteering at an assisted living facility, weekly, until his recent retirement. To be certified, he had to undergo training, have the disposition, and be
extensively tested. He has been great on the trail.
Old dogs, and even all dogs, easily learn. Your statement about the odds is completely wrong. Breed is not important, other than certain physical limitations, which is where knowledge and vets come in.
Remember "The Little Rascals," or their original name, "Our Gang?" Petey, their mascot and pal, was a Pit Bull. You can Google to find the stories about all of the dogs that were used by Michael Vick for dog fighting, that are now in loving homes with families and children, despite enduring extended torture.
It is the people, not the breed, that is the real rule that determines the outcome. The only reason that breed enters into the picture is because of physical limitations for tasks.
The first picture below is Slowpoke (that's his name) sitting on the lap of a resident (face not visible due to privacy rights) at the assisted living facility while the lady gets a haircut in the facility's beauty salon. I have pictures of my street dog in the wheelchairs, and in the beds of patients that are completely confined. The second picture is the day that he got his certification as a therapy dog. The picture from the previous post was from Mount Kearsarge in New Hampshire.
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