It is not only that they are paranoid, but it is because there are countries like Iran working vigorously for their nuclear program. If all the other countries decided to dispose of their nuclear devices and suddenly Iran has one, well then it will be a serious problem. For reasons like this, and because countries never trust each other enough and need their nuclear bombs and missiles as a deterrent, I really don't see this world ever becoming nuclear free.
They are some of the most powerful weapons in the world, and that is something countries really don't want to give up. Israel, especially being in the center of so much conflict, would not want to get rid of theirs. I hate to bring it up again, but with Iran developing nukes like there is no tomorrow is another reason for Israel to keep theirs. Because we know that Iran will probably never play friendly with Israel and if Iran were to figure out how to make an atom bomb, or even worse, a hydrogen bomb, the world would become a much scarier place.