We don’t encourage any on-leash greeting (i.e., allowing a dog to “say hi” to other dogs or people while leashed). Here is why.
Dog Socialization is not about saying hi to other random dogs and strangers while on leash. Doing so can be very counter productive.
We want to teach our dogs to be engaged, confident, and calm when we encounter other dogs and strangers in public. We want to have a well behaved dog who is a pleasure to go out with and one which will not cause other people or dogs inconvenience in public. That is our objective of socialization.
I know lots of people have been told that they should let their puppies/dogs say hi to a million dogs and people; but doing so can actually cause a lot of problems. It can lead our dogs further and further away from our objective of creating a well socialized dog.
Allowing dogs to pull to the end of the leash to whoever they see and then get rewarded heavily with affection from the stranger will teach the dog that prioritizing a complete stranger over their own handler/owner is the right decision, which is the exact opposite of what we want the dog to learn — to prioritize their handler/owner around other distractions at all time.
This will also condition the dog to become very stimulated once they see a random stranger, which will cause the dog to make a very big deal whenever someone comes to visit. The dog will have a very hard time trying to understand why all random strangers are sources of extreme arousal EXCEPT when they are ringing the doorbell.
On leash greeting is counterproductive to engagement training, which is the corner stone of good behaviours.
Engagement means the human handler should be the most desirable and interesting being at all time. The human handler should remain as the dog’s top priority even around heavy distractions. When the dog understands this concept, it is much easier for the dog to stay calm and attentive while laying down at a coffee shop, walking in a farmer’s market, shopping, flying, camping, hiking, at the vets, in a pub, and when guests are visiting.
When we allow random dogs or strangers to interact with our dog on leash, we have no idea what those people or dog may do. The stranger may do something that startles our dog (eg, a child may suddenly scream at the dog, an adult may accidentally drop a cup of coffee on the dog, etc.); the other dog may sniff our dog then suddenly acts aggressively a couple seconds later (i.e. suddenly starts growling, barking, or even tries to attack our dog).
We cannot really predict nor control what they may do but once this kind of things have happened to our dog, it will cause our dog to view those strangers/dogs negatively. Not only that, the dog will start to lose trust in the handler/owner as these incidents always took place under the watch of the handler/owner.
Since the leash is keeping the dog from defending themselves and moving freely, the human, who is holding the leash, is whom the dog will count on for protection in those incidents. When we allow things like that to happen while our dogs are on leash, we have failed our dogs. These negative experiences will compound over time, and eventually cause the dog to act out towards other human/dogs defensively, which is how a lot of dogs ended up becoming leash reactive.
Even if there has been no negative experience and the dog always enjoys greeting other dogs or strangers on leash, the dog will be conditioned to feeling extremely aroused whenever another human/dog is in sight - and “saying hi” will become not only an expectation but something the dog will grow to demand compulsively.
There will come a time when we cannot allow such greeting (e.g. we are in a restaurant and cannot let the dogs wrestle next to other patrons). When we try to stop such a dog from going up to greet another dog, the dog will feel really frustrated and may keep demanding to go by pulling to the end of leash, lunge on their hind legs, and bark very loudly. This is also a form of leash reactivity, which can cause the owner a lot of embarrassment and even injuries (e.g. some owners could get pulled to the ground when their dogs reacted out of extreme excitement this way).
As you can see, none of the above behaviours is what we would expect from a well behaved dog. Unfortunately, they are very commonly seen in dogs who have been allowed to greet other human/dogs on leash.
That is why we do not encourage on leash greeting.
Hope this makes sense.