Why are the three superpowers always at war according to the Brotherhood?
The three super states are exactly similar in ideology, philosophy and social system such that none of them, even if two allied against one, could conquer the other. Therefore, war becomes necessary in ensuring that each state maintains its status quo as propagated by the ruling class. In fact, if the citizens of the three super states were allowed to interact under any situation other than war, the results would be disastrous as they would realize the ideologies they were fed with about the inhabitants of the other states were false. The war between the three states is artificial as it only serves to help the ruling classes maintain the hierarchical societies already established. The real war however is between the ruling class and the masses whereby the ruling class utilizes the surplus labor of the masses to manufacture non-consumables thus creating a deliberate shortage of basic commodities. The discrepancies ensure the structure of the society is maintained. I hope this is helpful.
As long as there is War (whom it is with is of no concern at all), the people will live in fear of someone and will be dependent on the state they live in for survival. Since no country will ever win these wars (since that will work against the interests of each country), they create a kind of "peace," a stable situation. Psychologically, it's also useful to have an "enemy" to pull the people together. This is similar to the antagonism between Americans and Russians during the cold war.
A common enemy is a good thing, especially when you don't have to worry that the enemy will destroy you because you are useful to them.