Rocky has learned to invite play with small dogs by keeping a low posture. Notice his soft expression and low ears-- all designed to show peaceful intent.
1. Your Dog's Own Safety
Dogs who have been well socialized learn how to 'read' other dogs. They manage to avoid conflict by learning how to approach strange dogs, by telegraphing peaceful intention, and by using calming signals to defuse aggression.
2. The Safety of Others, Including human beings.
There are many things dogs only learn from other dogs. They learn to interact differently with dogs of different sizes or ages. ("Chase" may be fun for some dogs, while others prefer games that are a little slower or more gentle.) A knowledge of appropriate play can make a big difference at the dog park or when family visit.
One of the most important lessons taught by other dogs is bite inhibition. Any dog is capable of biting-- either another dog or a human being (as in "Keep away from my bone!"), but a well-socialized dog goes through a whole hierarchy of responses before resorting to a bite.
First, there's "The Look", then, "The Lip Curl". That may be followed by a low growl, then a snap. Even when resorting to a bite, the well-socialized dog will first nip. It's a pinching bite to let the other know that he means business. A penetrating bite is the most severe response. This is why it's important for owners not to punish their dogs for growling. If you take away steps 2 and 3, the dog has no other option but to jump from "The Look" to "The Bite". After all, he has to protect himself.
A confident Beau meets an equally confident Daisy.
Rude? Not really. In the dog world this behavior is perfectly acceptable. Deucey has learned to stand still when meeting other dogs, so that they can smell her.