The Battle of Britain took place during all those years when the Americans were throwing
Britain to the dogs.

Why was it the responsibility of the U.S. to protect the British? This was before NATO and the Truman Doctrine.

Did Britain "throw France to the dogs"? What is the nature of the 'special relationship' between the U.S. and Britain in 1940?

During the past 60 years Britain has certainly embraced the "I'm your weak little brother" school of diplomacy with the U.S., but the Britain of 1940 still had the arrogant trappings of Empire: confidence and power.

Don't project today's impotence on the Britain of 1940. Churchill always spoke eloquently and exhaustively about his beliefs. He does not need to be paraphrased by lesser modern minds with their Brexit whines of entitlement and empires lost.