My dd is afraid of dogs for the exact same reason others have described. We were at a playground where there were signs everywhere saying that it is not an unleash park all dogs have to be on a lead, fines apply. We’ve been there many times and there are many dogs off leash.
While dd playing happily at this no dogs off leash playground, a man entered playground with his kids and dog off leash. My dd screamed and ran to hide. (I have been working with her to help her overcome her fear).
I approached the man and started to ask “could you please put.. “ then he interrupted before I said “your dog on a leash”and said “no, she’s fine” quite firmly. I felt intimidated by him and turned to walk away, then changed my mind and turned back. I looked him square in the eye and said: “No, it’s not fine. This playground is purpose built for all children to play, including children who are afraid of dogs.” He then put his dog on a lead then yelled at me that he would have if I’d asked him nicely. I replied that we both know that I had asked him nicely, turned and walked away while he continued to yell abusively at me.
I felt shaken by this aggressive man. My dd seemed a bit scared of him too. Asked me why he was yelling at me. So, I had to try to explain and reassure her that we were ok and don’t worry about him but stay away from him.
It’s not the first time a dog owner has been aggressive or abusive over reasonable requests to control their dog or call their dog back, while my young child is clinging to me obviously scared.
I don’t remember this ever being a problem to this extent when I was a child. I grew up around animals including dogs. I remember people training their dogs to heel, sit, roll over, shake hands etc. Dogs were usually walked on a lead. Why has this changed so much in the last decade or so? Where did this entitlement come from, that my dog trumps your or your children’s personal space, safety etc? These owners also let their dogs off leash on the sports oval and won’t call them back when the dog runs into a game of football or other team sport. How bloody rude 
We also get the “don’t worry my dog is friendly” owners too. 