One supposedly "good" thing to come from the Cold War and the realization that more than one country had the capabilities to annihilate another with these weapons was the theory of Mutually Assured Destruction, or MAD. Basically, what MAD said was, why would it make sense for Russia to blow up the US, when the US would have sufficient warning of an incoming bomb, and could retaliate equally, or with more force, thus rendering Russia uninhabitable and economically ruined as well. There would be no victor, only two big piles of rubble and no one to answer for why we even started to begin fighting in the first place.
Since then, however, the globalization of the world, helped a lot by the Internet has made us much more aware of the potential devastation these bombs have. In World War II, you only really read about the bad Japanese from biased news sources and stories handed down. You couldn't address a Japanese citizen IN Japan, and say, "Hey, so what's your real story?". These weren't people to us I don't believe, in as much as they were faceless enemies, with women and children never even factoring into the equation. Now, you can turn on the TV, flip open the papers or turn on your computer and read/hear about the other side of the world, or even find out what people are like over there for yourself. The sense of isolationism is gone, which is essentially what we practiced around the time of World War II. All of that makes me think that nuclear weapons used on the offensive may never be seen again. Perhaps a retaliatory strike, but then that even leads to another point...who are these people that we really need to fear?
Kim Jong Il and Ahmadinajhad have both threatened to use nuclear weapons on the offensive, or first-strike. It bothers me that we even try to have diplomatic ties with either dictator since our new sense of globalization that has united us with the public from around the world aren't just nameless, or even faceless people anymore. I do believe that most governments consider the nuclear option not to be a viable one anymore simply because of the anti-humanity involved, so to see more than one person/government threatening it leads me to suspect that they have a superior feeling in their own humanity over that of their citizens, and the citizens of the rest of the world. Furthermore, in the case of an Ahmadinajhad or other radical Islamic faction, MAD doesn't work when martyrdom is considered Holy, and this should strike fear into the hearts of anyone who even knows where the Middle East is, regardless of your take on the War in Iraq, Palestine or Israel.
In terms of what happened from 1939 to 1962 though, I really can't say, and can't think of anything that would've been considered "outright insane" (<---did your teacher really word it that way?). The testing that was going on was pretty intense, and environmentally catastrophic, but we didn't know it at the time.
As far as rationality and irrationality go, look at nuclear power in general, and the quotes from Oppy and Einstein. I think it was one of them who said that this was the worst thing they ever accomplished, however, look at how far our understanding of radiation has come, and how much it does for us on a day to day basis. We don't even understand it wholly, but if we can figure out fusion, then we'll never burn another drop of oil again. So you could argue a lot of different ways about that particular point...its understanding and creation leads to destruction OR sustainability.
EDIT: "I have another question for you though, do you think that the Americans made the hydrogen bomb out of fear just like they did with the atomic bomb? you said MAD plays a huge role therefore nations create these weapons to show superiority but in the back of their minds they don't have intents of using them because of humanity reasons correct? "
You're probably in the best position to answer the original intent of the H-Bomb since you're into all of the actual research now (I'm going from memory). I don't believe that deterrence, or even the actual proliferation of an H-bomb is why it was made...I think that's just how it turned out. If I remember correctly, I don't think they even expected the bomb to work (again...I could be wrong...I think I've just been using H-Bomb and Atomic Bomb interchangeably).
As far as MAD, I think that theory was more of a product and result of the Cold War and is what eventually lead things to simmer down. In terms of new development, I think it depends. North Korea seems to be doing it in more of a "Look at me!!!" sense, where as Iran's president has made his intentions known on more than one occasion. Do we know how dedicated he is to this goal? No. For all I know, he could just be doing the same think as NK, but much louder, and in a much more terrifying way, so really, I don't know what these intentions are of the newest news in nuclear weapons development, but I don't think it's 100% MAD related.
I was talking about MAD more in the context of the Cold War, again, prior to the globalization of society with the Internet and cheaper travel. I'd HOPE that MAD still factors in today, but like I said, I have no idea what NK's intentions are, but Iran's rhetoric is anything but MAD-oriented (or, considering the practice of martyrdom, maybe it is, and it's actually desired? Could be an interesting tangent.)
Good luck. I know the History Channel just had something really good on this, perhaps chronicling Oppenheimer?