Partially yes, but there's an even more mundane reason; with nuclear weapons, if the other side has 5, you need 6: five to destroy their five, and one to destroy their capital. But when they discover that, they'll decide that they need seven: 6 to destroy your 6, and one to destroy your capital. Add in some uncertainty to that feedback loop, and an arms race immediately becomes an exponential curve moderated only by the amount of time production takes and the amount of resources each nation is willing to commit at any given time.
There's a very real way in which the proliferation of arms is, itself, an uncontrolled nuclear reaction.
Trying to be the change I want to see in the world.