The flag moved - The US flag that was displayed on a rod extending horizontally from a flagpole did not move because of wind (on Earth). It moved because of the astronaut's manipulation of the flagpole during his effort to drive it into the lunar soil.
Everyone involved lied! - Hundreds of thousands of NASA personnel and contractors might have lied and then kept lying about it for all these FIFTY years! This is as doubtful as things can get, particularly in these current days of leaks, self-publicity and social media. Over the years, several Apollo engineers, mission control personnel, and astronauts may well have lied about their precise involvement in the Apollo programme and, in some cases, their personal memories may be at fault but there are far too many people telling the same story. Faking a Moon landing would be easy, compared with the challenge of getting thousands of conspirators to maintain the lie for all these years!
The US lied because it was determined to win a public relations war with the (then) USSR - Clearly, the Soviet Union would have won such a war if they had exposed such a vast American fraud, but the Soviets were also technologically sophisticated in space. Their Luna 2 spacecraft had reached the surface of the Moon in 1959 - a full ten years before Apollo 11 made the first manned Moon landing. The Soviets knew the landings were real and they even acknowledged them.