I always thought them putting an American flag on the moon was a rather douchey thing to do. America can't just say they own the moon.![]()
They didn't say that. The Outer Space Treaty of 1967, of which the USA is a party, expressly forbids any single nation from claiming a celestial body, including the moon.
Think of it more as just a marker to say "we were here". The US was no more trying to claim ownership of the moon, than a climber who puts their country's flag at the top of Mount Everest is trying to claim the mountain.
I believe I read somewhere that the Apollo 11 astronauts saw the flag get knocked over when the Eagle lifted off.