Why can a lunar eclipse happen only at a full moon?

A lunar eclipse occurs only during a full moon because it requires the Moon to move into the shadow cast by Earth. This alignment can only happen when the Moon is on the opposite side of Earth from the Sun, which is the definition of the full moon phase.12

Eclipses do not occur during every full moon because the plane of the Moon’s orbit is inclined by about 5° relative to the ecliptic, the plane of Earth’s orbit around the Sun. Consequently, at most full moons, the Sun, Earth, and the Moon are not perfectly aligned in a straight line, meaning the Moon passes above or below Earth's shadow.12