The reason is the very legitimate fear of a rogue nation with an unstable or autocratic government trying to use nuclear weapons as an element of international blackmail or to deter retaliation for its own military adventurism. Which is more or less exactly what we see happening with Russia right now, so the fear wasn't unfounded. I mean, if we could have gotten Russia to give up their bombs too, we would have preferred that.

As it happened, Ukraine turned out to be less of a risk than Russia. Which is unfortunate. But the logical calculus is pretty clear.