Here's why:
* Centripetal means "center seeking".
* It's the force that keeps an object moving in a circular path.
* If the force were to act in any other direction, the object would either move away from the circular path or change the radius of its circular motion.
Think of a ball on a string being swung in a circle. The tension in the string is the centripetal force, constantly pulling the ball towards the center of the circle.