Why No means Maybe

After reading and blogging about Gift of Fear I begin to see why there may be a culture where "No" means "Maybe".
1. From young whenever our kids say No to something, we would counter with something like: Why don't you try it first? You'll never know until you try.
2. We try to teach cooperation and compromise until it becomes a habit. A No means no compromising which we teach them to be something possibly rude or selfish.

How should we teach our children when it's okay to say no, how to differentiate the situations where it is okay to say no, and importantly how to say no. Only when they feel that saying anything other than No would threaten their safety? But safety of the body or the mind or both? I can say no because saying yes might make me uncomfortable even though I may not feel threatened - aggressive panhandlers along my usual route for instance. If I say no they may become aggressive. If I say yes and give them a dollar they might ask for more. Is it okay to say no in this case? I might be uncomfortable saying both yes and no.