To answer your question of "Why does the far right like war so much" The answer is fairly simple. The Ancient Romans believed that the best defense was a good offense. Whenever they felt as if they were being threatened, they attacked. Why does that matter? Ancient Rome was a significant, although idealized, source of inspiration for modern conservatism. For one, America is very threatened by Iran. Iran is notoriously known in America as a "State Sponsor of Terrorism" for good reason. The right wing also believes in peace through strength. I'm sure that any American military base in any other country is not only there to protect America and its allies, but to intimidate and discourage people from attacking the US. The right wing has a pro-defense culture as well, leading to people joining the military for no reason other than their political beliefs and the desire to protect our nation. Why is the far-left (Liberals, Democrats, Communists, etc.) so anti-war? This is the real world. Diplomacy does not always work (such as the peace talks that were shut down with the attack of Pearl Harbor). Diplomacy without the backing of force is just a request. Boots on the ground is a very real, very necessary thing to create a safe place for your own country, and the sooner the left can accept that the better. In the lefts mind, the world wouldn't have any militaries, or governments, or borders, or anything, which is basically Marx's vision of communism.
The only way to truly be at peace is to be so overwhelmingly powerful that no rational country would dare attack you, and idea made popular by the legendary Ronald Reagan