Here's your basic thought process:
Early on, the technology and science to make it was discovered. THEN it was a race to be the first one with it, to then basically use it as a threatening device and possibly even to use it as the pure raw power and what could come of it probably wasn't as well known or realized.
ONCE we saw the devestation, what it truly could do...and more countries got it...things changed.
It became one of those things that "That country has it, which means if we get in a conflict with them they have the trump card...nuke". Its kind of like playing poker with someone and at any time they can declare that all thier cards are wild. If you both have that power, then it becomes a normal poker game again because if one tries to use the "everything is wild" ability then the other can and it stale mates.
So one country has it, the countries that may be near them or fearing of them will want to get it. This way they are as afraid of launching thiers, as you are of them launching thiers, because they know when they do thier having one come thier way as well.
I'm not saying its a GOOD defense, or a good thing, but its why its prolificated as it has. Its why iran wants to get a nuclear program because israel has one. Its the whole deal with pakistan and india. It is the reason for the cold war.
There is actually a theory going around scholars of weapons prolification that it could actually be BETTER for us to basically let every nation trade and create nuclear weapons and have them, thus basically "assuring" in thier mind the general thought that NO ONE will launch.
Not saying its a good theory, but its an interesting one if you want to look into it. I'll try to post in and around here more on this as i go farther in a class i'm taking currently. Its a politics of weapons prolification class and the professor is one of the most intellegent men on this subject i've ever met