Why does a ray passing through optical centre remain undeviated?

Look at the lens as a slab of finite thickness. In a small vicinity around its center we may consider its opposing surfaces as parallel to each other. A ray incident on this area, at any angle, will be refracted twice at parallel interfaces. Therefore it will emerge on the other side of the lens on a direction slightly displaced, but parallel to the incident one. Since the parallel displacement is tiny as long as the lens is not too thick, it looks like the ray passes through the center undeviated.

Truth is that the light does not pass through undeviated,we just assume it passes through undeviated, this is because we make the thin lens assumption.we assume that the lens we are dealing with is thin and in such lenses,when light is directed towards the optic centre the light ray refracts once while entering the lens and the second time while exiting the lens but since the lens is thin the light wouldn't have travelled a large distance in the lens therefore when the light exits the lens the amount of deviation from the path light would have taken if there were no lens would be very less( very negligible ) ............butto keep things simple we say just say that the light ray passes through undeviated.

But keep in mind , as the lens gets thicker and thicker the deviation will become larger. ;)