> If NATO had met the Russia's demands, wouldn't the invasion have been prevented?

Probably not, in the long term, and the ability to prevent similar coercive efforts against other nations near Russia would be far less.

> I don't understand how the west didn't see that they should at least accept to exclude Ukraine from NATO.

What would the world have got in return from Russia? A solemn promise, a ratified agreement in writing and everything, that Russia would make no demands or incursions on Ukraine's sovereignty and territorial integrity?

Yeah, something like that would be great.

Except that's what the world already got from Russia, in exchange for Ukraine giving up its nukes back in the 1990s. And look how much that piece of paper was worth.

because caving to totalitarian dictators has historically incited them to decided to take over Europe.

This is an important point

Maybe there was a chance for a solution without invasion. But it seems West did not believe/want this. Either this was because West not wanting to look weak or they have a secret plan and wanted Russia to invade... Either way, Western actions leading to this weren't in Ukraine's best interest.