What you learned in school
Astronomy textbooks taught that the Moon formed alongside Earth from the same primordial material during the solar system's creation. Students learned about the "sister planet" theory of lunar formation, where both bodies condensed from the same cosmic dust and gas. This seemed logical given their proximity and was the accepted explanation for decades before Apollo moon rocks were analyzed.
What we know now
Astronomy classes taught that the Moon formed from the same material as Earth during the solar system's formation, or that it was captured by Earth's gravity. Students learned about the "sister planet" theory of lunar formation. Analysis of Moon rocks brought back by Apollo missions showed significant differences in composition between Earth and Moon materials. The current leading theory is the Giant Impact Hypothesis - that a Mars-sized object collided with early Earth, and the debris from this collision eventually formed the Moon. This explains both the similarities and differences in composition.