That's exactly it. When most parents talk about 'teaching' their kids about 'sharing', they're talking about situations like:
1. Your child's toy is taken ('snatched') by another child. Your child starts to cry (understandably). You tell your child "no, no, share your toys." or "it's his turn now."
2. Your child snatches a toy from another child. You take it from your child and give it back to the first child. You tell your child "no, no, share the toys." or "it's his turn now."
See how that would be confusing for your child??? In both situations, "sharing" means YOU LOSE YOUR TOY. Only rarely is a child in a situation where they are on the "receiving end" of a "forced sharing." So they learn that sharing is a NEGATIVE thing from their perspective, and don't learn what it truly means.
And when it DOES happen that your child is on the receiving end of sharing, it's usually in a context where your child will end up with a "haha, I won that battle" kind of attitude. So you get situations where your child wants a toy another child has, and your child starts demanding "Hey you have to SHARE!" or "mom he won't SHARE with me!!!"
Forced sharing teaches selfish motives for sharing, not spontaneous affection or fairness.
Another fact is that kids/toddlers of a certain age are just starting to understand and integrate the idea of personal possessions, as well as ideas of fairness, and of power vs helplessness in fulfilling their own desires. Wanting to keep a toy for themselves is a natural part of their development and is not "selfishness" in the adult sense of the word. Forcing kids to give up their beloved toy in the name of "sharing" goes against their developmental abilities and isn't necessary either. It's not a selfish sin that needs to be broken out of them, in other words.
We've never "taught" or "made" DD share. We do mention it when she shares spontaneously, by thanking her for instance. She shares quite a lot, in fact. Still has her "mine!" moments, of course, but as I said, that's a natural development. She's figuring out that things CAN belong to her, and that's an important thing.
But it's certainly not about DIScouraging sharing. No more than, say, not holding your 6mo infant in a standing position for an hour each day and moving their legs in a walking pattern and trying to force them to bear their own weight would be discouraging walking. It's not something you need to force.
EDITED TO ADD: I wanted to reiterate and emphasize the PP's comments in regards to teaching sharing BY EXAMPLE. Children learn by example, by imitation, first and foremost. If you always are asking THEM to share, but never having them be shared WITH, then they don't learn it as a positive thing. When you all share with each other, then they will naturally pick up on that. I suspect that's why DD is so apt to voluntarily share her stuff. That's how she's always seen it done around here.