@Corgiowner I think @CoubousAndTourmaIet has summed it up well with this:
But I suspect a lot of her comments are based on the average first time owner, whose kids are not dog savvy and who may struggle with knowing what the boundaries are. I don't think it's as cut and dried as saying "nobody with kids under 10 should ever have a dog".
I also think @Corgiowner your background is very different to the average person looking for a first dog, or has young children. Most, in my experience, are young professionals who have no idea what the hell owning a dog entails (thinking they can shove it off to day care 5 days a week from week 12, not realising mouthing is a thing etc).
I spend a lot of time dealing with Golden Retrievers who have been sold to people with young children completely ill-equipped to deal with such a large dog (particularly one that stays young so long and is also, unfortunately, incredibly sensitive) and therefore end up 'ruining' the dog or failing to control their children and thus the child gets bitten. Out of the last 8 dogs we've had come in, 7 of them were due to bites on young children and the other one was because the owner died.
Very often, my experience of people who bring in these dogs is they have no idea what they were getting into, thought the dog would be their kids best mate, failed to exercise and train it due to lack of time...and these are all things a good breeder would have realised if they paid any attention and asked any questions. People with young kids (particularly multiple ones) do not really have the time to spend on raising a healthy, happy, dog. Except they don't go to good breeders - they go to greeders.
I am (for lack of a better word) incredibly militant on it and most of the breeders/people involved in the rescue I volunteer with are as well - not because we don't think people with young children can make good owners, but because it's just not a risk we want to take.
Sadly, too many owners these days fail to understand that dogs require attention and dedication - they're not toys your kids can cuddle and fuss - and thus they fail to give the dog what it needs, and that's when accidents happen. It's very different to twenty or thirty years ago.
The reason the breeders I know, and would recommend, aren't willing to sell to families with young kids is because we love our puppies to much to take the risk of them suffering through neglect - so we sell to experienced people, with older kids, who we trust will be reasonable and practical.
Perhaps if I was a 'greeder' who just wanted to make money, I would think differently. But I love my dogs and the puppies to much to take a chance on their future - and I think good breeders should feel that way. Why settle for a 'silver standard' future for your dog when you have the option to give them gold?