I think that just in general once people have children, they think it gives them a license to suspect anyone of anything if they feel like it. I remember sometimes when I used to walk my border collie and there was a family coming the opposite way they'd cross to the other side of the street or something - as if my border collie is going to maul them.
The danger is very real. Don't get me wrong, I love dogs and have had many wonderful dogs as pets. I am also quite talented at training them, but there is always the possibility that a dog may react badly to a stranger, if it feels threatened. Children who are not aware of a certain dog's demeanor will often make mistakes which could make the dog feel trapped. Braindead parents who allow their kids to walk up on a strange dog are being irresponsible.
Most of the problems are caused by the kids, themselves, though. My kids have been taught how to approach a dog and "introduce" themselves, but they still get stimmed out by them. I usually cross the street, too, but it is mainly because my kids get severely overstimulated by big dogs and the dogs sense this. It is not fair to the kids or the dogs to force them into stress.
I have seen what happens when a dog bites a child, more than once. A dog can quickly produce gruesome injuries to a small arm or leg. One of my favorite dogs had to be put to sleep, because it bit a child. It was a very bad day for me, but he did bite the kid and a rabies test was ordered by the court, that same day. It happened to be a kid who had taunted my dog through a fence for weeks, but that did not matter. I trusted that dog more than I trusted any human, but he defended himself and was destroyed for it.
phobia.