Perhaps history will shed some light on the matter.
The US has been the only nation to use nuclear weapons in acts of war: Hiroshima and Nagasaki. But after that, the US seems to have acted quite responsibly, often acting as if it feared its own weapons (with good reason, actually). Other countries have had nuclear weapons and most have acted responsibly. I think the issue in the minds of many governments is the
PROLIFERATION of nuclear weapons, especially to unpredictable, often unstable governments.
Of course some would contest that the current nuclear powers have always been responsible or stable. The Soviet Union broke up, leaving the possibility that some nuclear weapons may be stolen or sold off. Some would say that Israel came within inches of nuclear attack (I read that they had already launched their fighter-bombers in the 1973 Yom Kippur War before they were recalled). And how stable is a nuclear face-off between India and Pakistan? And what about the paranoid, xenophobic government of North Korea!!?
This is not a simple issue, to be sure.