This debate rolls on because so many people on either side refuse there is some grey area and bad behaviour on both sides.
Some examples...
Walking a small terrier (on lead and well under control) about 5 years ago, a child and her mum stopped and asked if she could pet him. I said yes but to go slowly so that he isn't afraid. At that point the child reaches round his middle and attempts to pick him like a rag doll. Luckily the dog is well behaved and struggled rather than snapped. The mother just laughed until I sternly told the child to 'Put Him Down'. At that point the mother grabbed her child's hand, causing her to drop the dog on the floor. The dog had a sprained leg from that fall that took two weeks to heal.
Walking my springer puppy when he was much younger - again on lead and close by my side - and 5 young children ran up to him, surrounded him and tried to all pet him at once while he cowered in the centre. I instructed them all to "Step back you are scaring him" at which point one of the mothers proceeded to (try to) lecture me that they just wanted to pet the puppy and he would grow up fearful of children unless I socialised him properly - that I should just "relax a bit".
In both those scenarios, the children could have had a nice experience with the dogs - initiated by them - if they had known how to behave around dogs or if the parents had taken the time to explain to them.
In contrast, only the other day a boy stopped and asked very nicely to pet the springer. Despite mum saying he was autistic and didn't really understand dogs, he did everything I asked (stand still, hold his hand out so the dog could sniff etc) and the mother backed me up. Both dog and child had a very pleasant encounter and went on their way.
It's also worth saying in none of those scenarios has my dog been allowed to approach a child uninvited - no dog in my care ever is. For the dog's safety (and probably a bit for the kid's), they are on leads when children are nearby: always. In fact, a walk where we don't see anyone else at all is one of my favourite types of walks
.
There are dog owners that think everyone should love their dogs and that the dog is friendly. There are also parents who think that their children have the right to pet any strange dog they want to, just because it's cute. A bit of respect and responsibility on both sides wouldn't go amiss.