I'm with KB on this one. I dislike dogs, and always have done, and I'm from the school of thought that they should be on a lead in a public place. I resent having to restrain children to enable dogs to run free.
Whether or not any harm is likely, some of us just don't share a dog owner's love for their pets and their furry friends, and really feel uncomfortable when dog owners take personal offence that I don't want anything to do with them. People don't get upset if we don't like their choice in shoes or cars - yet many dog owners seem to see we dog rejecters as a personal challenge. My own DH had dogs as a child, and can be a bit like this, and it really irritates me.
From the safety angle, this has been done to death, but... YOU may be certain that your pooches are lovely friendly chappies, but I can't tell them from the majority of less-than-perfectly-controlled dogs that roam parks. A thunder storm isn't ever going to rip your daughter's face off. A dog might.
In answer to the inevitable "mine are beautifully behaved and wouldn't hurt a fly" comments, from what I can see, and from the plethora of "It's me or the dog", "Dog Borstal" stuff on TV, there are sadly more dogs that are not fully under control than there are obedient ones. I'm sure that there are many reasons for this - including the scary tendency of some owners to use their dogs as surrogate and very spoiled children, or the more thuggish tendency who like their dog to be as hard (ie feral) as they perceive themselves to be. Either way, I don't want them near my children.
And with that said, a dog in friendly mode is not necessarily to everyone's taste either - I'm just not into any slobber or jumping up or sniffing that isn't coming from my children. (and I'm not even too fond of that, at times!)
My DD (2.7) knows never to touch a dog unless I have said that she may. At the moment they do freak her out, but so do a lot of other things.
Annner