You misspelled defeated.
You should care. If the UK had not won the battle of Britain, Hitler would've taken over. He would then fail to take the Soviet Union. In short, if the UK hadn't won, the entirety of Europe would be communist. Your welcome. The UK also prevented D-day from failing due to them keeping it a secret. Your welcome. Finally, the UK cracked the Enigma code, shortening the war in Europe by 2 years. Your welcome.
We are also your allies due to NATO, and, while we don't have as many subs as you, Vanguard subs are generally better than Ohio ones.
You probably should care