An argument I have heard in the past, but only occasionally agree with, is that a movie is only as good as its quotes. Though Dr. Strangelove is more than the sum of its parts, one can't ignore the dialogue when searching for the soul of the movie.
A fine quote for the era of the film's setting is "deterrence is the art of producing in the mind of the enemy...the FEAR to attack." Perhaps if we applied this philosophy, Hitler would not have run such a muck. Fear, as we all know, is one of the most powerful weapons an army can possess. It is the only real reason that the final scene was not ours. Strangelove later argues that the Doomsday machine should have been announced to the world.
For all the polygamists at heart, there is "the ratio of ten women to each man. Now, wouldn't that necessitate the abandonment of the so-called monogamous sexual relationship." As Mr. Bennet mentioned, this movie is all about sex. The point of sex is to reproduce, which is the point of life, from an evolutionary stand point. Perhaps this is Stanley Kubrick's philosophy on love (With eccentric films like "A Clockwork Orange", "The Shinning", and "2001: A Space Odyssey", it would not surprise me).
The capitalist can appreciate this one: "Do you realize that fluoridation is the most monstrously conceived and dangerous communist plot we have ever had to face?"
Like much of the film, this is a satire. Fluoridation is one of the most harmless communist concepts that exists. Because it is a public project that would influence everyone in a given nation. It is merely the level of control that would frighten the die hard anti-red person. The fear discussed in the first quote is responsible for both the inability to attack and the desire to do the opposite.
Finally, the historian gets a bone too: "[C]ome over here, the Red Coats are coming!" Ironically, the color of the enemy that began and ends our existence is red. The director chooses this line, probably to show how our roles as the victim, and now the bully, has changed over the centuries. We are the ones attacking the Russians and we have the nerve to call them red coats, though we technically did that to them too, but we had better reasons.
What I can gather from these quotes is that "How I learned to stop worrying and love the bomb" is a satirical, yet deep film. Though it pokes fun at the military institution of the 1960s, it also puts it in perspective.