How can an argument be made that an arms build-up-might lead to peace

I am posting the same answer I gave to the other student asking him the exact same question;

At the end of the Cold war the USA, in essence, ran an Arms Race for one. The method is deterrence-to make such a large arsenal of weapons that for any other nation to build up arms all but useless. With one dominant arms force to act as the world's policemen, for other nations to fight in any way would be all but, as I dare say again, useless. What nation would want to fight if they know that an army with 100x the men and the most modern technology would step in and fight them back?

Again this all theoretical and despite the size of the US army, geopolitical and domestic realities make this argument dormant.