Newton's first law.
An object, released to free motion, will move in a straight line, unless prevented from doing so by a force.
youtube video uploaded by Yuri Kovalenok, demonstrating bulging of an elastic spherical object when subjected to rotation.
Initially the parts of the sphere close to the equator do not experience sufficient centripetal force, so their initial motion is not purely circumnavigating motion. Instead their motion is a vector sum of a component of circumnavigating motion and a component of motion in a straight line. As a consequence the "equator" recedes from the axis of rotation.
The object is elastic. The bulging deforms the object and the elasticity starts to oppose that deformation. After some bulging has set in the elasticity of the object provides the required centripetal force to prevent further bulging.
The video is gorgeous; I took this question as an opportunity to link to this video.