When the U.S.A. entered World War 2, Churchill managed to persuade Roosevelt to put Germany first. Astonishingly, Roosevelt agreed to this.
Now think of it like this.
Japan had already attacked the U.S.A. Germany had done no such thing. As far as Hitler was concerned, the U.S.A. were a nation that could not be invaded - separated from Europe by thousands of miles of Atlantic ocean. Germany was of no immediate threat to America. It's true that the Nazis had officially declared war on the U.S. but so what? Why on Earth would the U.S.A. want to concentrate most of her efforts on fighting Germany? Theoretically it wasn't even their war, yet Japan was.
Of course, in terms of good and evil and the course of prophecy, Hitler was far more dangerous. He wanted to exterminate the Jews and he eventually teamed up with the Arab Mufti al-Husseini and between them they had a plan to wipe out all Jews in Europe and the Middle East. God would have known that even if nobody else did..
I think Churchill was divinely inspired to persuade the U.S. to concentrate their efforts on Germany. Churchill was a Christian, albeit a flawed one and even if he did not know what he was doing or why - I believe that he was led by the Holy Spirit to speak out for the European cause.
I also believe that Hitler declared war on the U.S. for the opposite reason. Sure, he'd made a pact with Japan but Hitler was never good at keeping pacts. Look at what he did with Stalin.
Hitler declared war on Germany because Satan whispered in his ear and convinced him that the U.S. could be defeated, even though it was an almost an impossible task. With a Nazi victory, Hitler would then have been in control of the three main areas of Jewry - Europe, U.S.A. and the Middle East. The descendants of the Tribes of Israel could then have easily been exterminated and Biblical prophecy would not be fulfilled. Satan would have known after the Balfour declarations that reconstruction of the Jewish state of Israel was just around the corner and he desperately needed to finish the Jews off before this happened. Once the Jews had their own state, their own resources and their own armed forces, they would be much harder to destroy.
Of course, the Nazis failed and sure enough, just three years after the war finished Israel was officially recognised as a new nation.