1. Your dog isn't actually friendly.
If your dog is stiffly approaching mine in a straight line with all the hair on her back standing up and her head and tail held as high as possible, she isn't coming over for a friendly greeting and I can tell that even before she starts growling. If she were truly being friendly she would be all curvy and waggly with her head and tail held level or low, and she would be walking towards my dogs in a big arc. If your dog takes the stiff-and-direct approach she's not coming over to say hello, she's trying to show my dogs how big and scary she is. On their leashes my dogs feel cornered and intimidated, and if your dog doesn't give them their space they will attempt to defend themselves and we will have a dog fight.
2. Your dog is socially retarded.
If your dog was truly friendly, he would understand how to take 'no' for an answer when attempting to meet a new dog. My dogs are not subtle about their desire to be left alone, and a well-mannered friendly dog will figure that out and pass them on the trail without getting too close. Your dog's continued approach is a lot like being cornered by a stranger holding their arms out and saying "Hi! Give me a big hug!" If you're polite you might indulge them, but if you've had some bad experiences with grabby strangers you might just hit them if you can't run away. The brings me to my next point:
3. My dog has a bad back.
Awesomedog has had spinal disc problems since he was under a year old, and he's seven now. He does not want to wrestle around with your large dog. Unfortunately, your dog may not figure that out until he has invited Awesomedog to play by way of bodyslamming. "But he only wants to play!" you protest as I kick your dog in the head and shout incoherently about vet bills. This is the dog equivalent of your hefty third-grader charging up to my frail kindergartner on crutches and shouting "Tag! You're it!" while he sends my kid sprawling. Yeah, he just wants to play, but he's out of control and can hurt other dogs. This kind of painful greeting is exactly why Awesomedog is afraid of other dogs when he's on a leash and reacts violently when they get too close.
4. My dog is stupidly tiny.
Tinydog weighs about 6 pounds, and he finds large dogs extremely intimidating. Some dogs figure this out and give him some space, but many completely disregard his attempts at communication and simply tower over him while sniffing. Sometimes Tinydog explodes in a ball of teeth and yapping and terror and rage. This can be effective, but sometimes it just triggers the bigger dog to attack. If your 80-pound dog decides to bite my 6-pound dog, mine if probably going to be seriously injured or even killed. This is why I am not comfortable having your off-leash dog wander over for a casual sniff, and you shouldn't be either. I don't know what your dog is going to do when he wanders over, and you don't know how my dog is going to react either, this is not a risk we need to take.
I understand that people like to let their dogs get as much exercise as possible when hiking, and I'm not a huge fan of following rules just for the sake of following rules. I keep my dog leashed on the trails because Awesomedog wants to bite everything with wheels (mountain bikes, baby strollers...), Tinydog doesn't actually come when I call him, and not everyone wants to meet and greet my dogs. I don't really have a problem with the well-mannered dogs that are under control and closely supervised by their people and happen to be off-leash, as long as those people are respectful of my dogs and their need for space. It's not just my own dogs, either. Most dogs aren't entirely comfortable being approached by a loose dog while on a leash, even if they're perfectly friendly when both parties are loose. It's just polite to keep your off-leash dog from approaching a loose one, no matter where you're walking.
