dogs not allowed? Why?

Why are dogs not allowed in so many places? Is a well trained dog more irksome than a disobedient child? I just want to know why so many places, beaches, lakes, hotels, parks are forbidden for dogs -yet the same places allow the most extremely, ill behaved, bratty,horrible children to run rampant over the other guests and property. I have stayed in parks where children threw rock at ducks or other animals, including each other, damaged property, rampaged all over.I have been in restaurants where they stood on the chairs throwing food at strangers and tripped up the waitstaff, in hotels they have taken over the elevators,playing at riding up and down, pushing all the buttons.When called on their behavior, no one, parents , or staff corrected their behavior. By the way I raised 3 well behaved daughters and I love children -just not brats.. So my question is--- why should children be allowed in these places without a damage deposit, this would be fair and equal to the deposit I must pay for my dogs.Why are dogs forbidden? In Europe dogs are allowed with their masters in restaurants and no one minds.. What is different here?