Here's why:
* Centripetal means "center-seeking."
* The force is responsible for changing the direction of the object's velocity, keeping it moving in a circle.
* If the force didn't point towards the center, the object would either fly off in a straight line (tangent to the circle) or move in a spiral.
Think of swinging a ball on a string. The tension in the string provides the centripetal force, constantly pulling the ball towards your hand (the center of the circle).