Why does a ray passing through the optical centre of a lens goes undeviated?

Answer 1

This is true in the thin lens approximation, which is the one most commonly used. In this limit, the front and rear lens surfaces are parallel in the center, so there is no deflection. When imaging an extended object, this is true regardless of whether or not the ray goes through perpendicular to the surface, so the previous answers are incorrect.

Answer 2

Because it hits the surfaces perpendicularly, refraction does not alter its angle.

Answer 3

it goes through perpendicular, and the angles are not bent