Unleashed dogs are a huge problem everywhere, not least of all Manhattan. I manage a team of dog walkers and one of the most common problems they face is idiots who walk their dog(s) off leash on the streets. They run up to our dogs and more often than not, it results in some kind of ruckus. A lot of these morons have aggressive, hostile dogs who should be muzzled let alone leashed.
But regardless of temperament, when an unleashed dog encounters a leashed dog the potential for a brouhaha is always there. I think it has something to do with the clash in body language between leashed and unleashed mutts. When they're unleashed, they're restricted in the kind of body language they can show each other and when one dog is giving it the full "Hey whatcha up to" and the other isn't responding as they should, wires get crossed.
You also have to think about people who are terrified of dogs. To such people, the sight of an unleashed dog approaching them is one the scariest things they can imagine - even if it's a toothless old chihuahua with its paw in a sling. And of course dogs usually detect fear...