Why did Earth end up with one large moon instead of a swarm of small ones?

Answer: A giant collision’s debris could merge into one large moon.

A giant collision’s debris could merge into one large moon. ✓ — Correct. Early Earth was struck by a Mars-sized body, and the impact threw rock and dust into orbit. That debris gathered into moonlets, then merged into one large moon. Apollo samples support this: the Moon’s composition is close to Earth’s mantle and it was very hot early on.

Earth could capture one passing body and hold it as its moon. — Wrong. Capture does happen: Neptune’s Triton is probably a captured body, so this idea is not wild. But the Moon’s composition is very close to Earth’s mantle, which is hard to explain if it formed elsewhere. Giant-impact debris fits that evidence better.

Earth’s gravity could keep only one moon in a stable orbit. — Wrong. Gravity does decide which orbits last, so the idea has a grain of truth. But it does not set a one-moon limit: Mars holds two moons, and Jupiter holds many. Earth’s single large moon came from impact debris, not from a gravitational cap.