Men free from fate?

[CAB]

I was going to post this question on the philosophy thread, but they seem to have quite a lively discussion going on there now, so…

It is said that Men are free from fate, but all of the other inhabitants of Arda are not. How could this be possible? I don't see how beings (or for that matter, even inanimate objects) who are bound by fate could exist as such among people who are not.

For example, say a particular Elf is fated to shake a certain Man's hand at a certain place and time. If things work out this way, then wasn't the Man just as fated as the Elf? On the other hand what if the Man decides not to be at this certain place at the certain time? How can the Elf then do what he is fated to do?

Another example, this time not involving any direct contact between fated and unfated people: What if a Dwarf was fated to pick up a particular rock one day, but some uncooperative Man had come by a week earlier and thrown it in a lake? The Dwarf's and rock's supposed fates couldn't happen.

Was Tolkien's world containing fated and unfated beings impossible or am I missing something?