Both are correct. One is British English (with the "s") and one is American English (with the 'z') If you are writing for an American audience, use "organization" (as well as color, behavior) Otherwise, use the British spelling. In either case, people will understand.

The first answer is correct and I’ve used both. It’s pointless to ask why or why not. Just accept the fact. It’s the English language.

The one with "u" is British English, the one without is American. American uses "z", British uses "s".

British English has an insane mixture of -ise and -ize endings that you must simply learn, or not as in my case. The Americans seem to have simplified most things that require memory to simply use -ize every time. The others, such as, colour --> color were simple misspellings that became standard in Anerican English. As said below, choose your audience, but few will be offended by the other. Do however expect a deep-seated compulsion for people to correct to the ones they think are "correct". :)