How do you spell this word, chosen at random from a dictionary? Is it 'organise' or 'organize' ? Organize is correct, according to the Shorter Oxford Dictionary, and is its main entry for the word. The word comes to us from Old French 'organizer' and Medieval Latin 'organizare' ( not only a word not in Classical Latin, but with Z which it never used, except in words borrowed from Greek). But modern French uses 'S' in the word and so, sometimes did we from the Late Middle English period, and the 'S' version is given as a secondary spelling in the Dictionary.
I was taught to use Z in this and many other words where S is now commonly used; it's a bit of an effort for me to follow the current fashion for 'S'. If Americans prefer the Z version they are doing no more than we used to do. We shouldn't blame them for it.