The Moon is being pulled toward the Earth, but it’s forward momentum causes it to miss Earth each time it goes around by a wide margin. This is called an orbit.
However, let it be known that because the oceans slosh around on Earth as it rotates about it’s axis (these are called ocean tides), the speed of Earth’s rotation is gradually slowing down. Billions of years ago a day on Earth was only about 8 hours, and now it continues to slow down. We compensate this twice a year by adding leap-seconds as needed.
This slowing of the earth’s rotation causes the moon to drift further away from us every year by about 1.5 inches, so eventually the Moon will escape Earth altogether and drift away.
It will never crash into Earth.