before i say anything, i'm just looking over this with a critical eye so don't take offense to anything i say
"co-existing on many different levels and many different races"
why levels and races? doesn't make sense
"Society forty years ago was much different from the world we live in today. Many people lived in fear of what would best be described as: the end of the world."
It makes sense kinda, although I wouldn't use the colon.
". Living in North America gives us the nice ability to go to bed without much fear for a bomb exploding on our house or getting on a bus without fearing it being blown up by a man who’s had enough listening to people talk about “peace.”"
too long-winded for one sentence
"Now that we are in to the 21st century, we see that the results of using deterrents as a method of piece only provides more alternatives against peace in the end."
how so?
overall, you state that the world shouldn't rely on deterrence without describing what deterrence is. you should explain more on the thought processes of the governments of america and russia (ie: why bombing the other would suck for them), public disapproval at home, what a bunch of nuclear bombs would actually do to the enviroment that makes it so devastating, etc.
you should also add more examples of deterrence used in the past and what deterrence would be used for today.
"All in all, humankind today has advanced well enough to be able to imagine much more effective, and safer methods of peacekeeping and deterrents than nuclear destruction."
this is a pretty grand statement that's pretty much equivalent to "we should know better than to war on each other".
on the plus side, your essay uses a lot of imagery and it flows reasonably well
"Especially in the case of the Cold War, mutually assured destruction may provide a temporary peace, but the aftermaths of such a “peace” only lead to more violence."
i guess if you wanted to get technical, the whole world would be at peace after a nuclear war. and explain what you mean by "aftermaths". you mean like the vietnam war as fighting against communism, or something post-cold war like the problems of reunification in germany?
good luck!