Gravity indeed pulls everything toward the center of the Earth, but the reason we don't see objects being squished or flattened is due to the balance of forces involved.
Gravity is a force that acts uniformly on all parts of an object, pulling it toward the center of the Earth. However, objects on Earth's surface also experience an opposing force known as "normal force." The normal force is exerted by the surface supporting the object and acts perpendicular to that surface.
When you place an object on a surface, such as a table, the normal force from the table pushes upward to counteract the force of gravity pulling downward. These two forces balance each other out, resulting in the object maintaining its shape and not being squished or flattened.
The normal force adjusts itself according to the weight of the object. As the weight of an object increases, the normal force also increases to counterbalance it. This is why heavier objects feel "heavier" when you try to lift them—they exert a larger force on the supporting surface, requiring more effort to counteract gravity.
It's important to note that the strength of an object's internal structure also plays a role in its resistance to deformation. Solid objects have cohesive forces between their particles that help maintain their shape under external forces, including gravity.
However, in extreme cases such as very massive celestial objects like stars, where gravity is significantly stronger, the gravitational force can cause compression and deformation, resulting in squishing or flattening. But for everyday objects on Earth's surface, the forces are balanced in such a way that we don't observe significant deformations due to gravity.