A rescue centre says it has been contacted by the owners of several rottweilers whose owners no longer want them after a boy was mauled to death.
Ministers have rejected calls to review the Dangerous Dogs Act
Archie-Lee Hirst was killed at his grandparents' home in Wakefield, West Yorkshire, on Saturday.
Many Tears Rescue in Llanelli, Carmarthenshire, said it had taken in four rottweilers and had calls about a further nine it could not accommodate.
But owner Sylvia Van Atta said getting rid of dogs was a "knee-jerk" reaction.
Ms Van Atta said people had been calling to say: "We have grandchildren visiting, we can't possibly risk the dog.
"I asked: 'Has it done anything?' They said no."
All the dogs were under two years old and from owners in the Swansea area who had them since they were puppies, she said.
Media reports about the death had focussed on the child and not given the "other side of the story," said Ms Van Atta.
She said: "Really, man has an awful lot to answer for in dog attacks that is not being addressed, not being published. The dogs get blamed for everything.
"People haven't learned about what to put in their sitting rooms. They don't understand dogs."
Archie-Lee Hirst's family are said to be "inconsolable"
Ms Van Atta said the blame lay with those who sold such dogs to "anybody", did not carry out background checks and sold them without stipulating they had to be castrated or spayed.
She added: "If you are going to have a dog that has a guarding instinct, give it nothing else to do, keep it on a chain, don't let it socialise... rottweilers know whether there is another dog in the house. All they can do is become territorial."
Sue Denham, from Llanybydder, Carmarthenshire, who has been breeding rottweilers for almost 20 years, said education was vital for owners.
But Ms Denham said that did not mean people would listen.
She said: "You do need to educate people. No dog - rottweiler, poodle, bichon - should be left alone with a child.
"That is, to me, common sense and I think to any responsible dog owner. They are an animal.
"And I don't think many people would put their young child in a field with a horse."
Detectives investigating Archie-Lee's death are focusing on house-to-house inquiries, speaking to neighbours and local business owners.