Question

why the ray passing through the optical center doesn't deviate

Answer 1

Actually the same happens when the ray passes through optical centre. This can be observed in a thick lens. In thin lenses the perpendicular distance between extended incident ray and extended emergent ray is negligible. So we can say that light ray passes through optical centre without deviation.

Answer 2

the ray passing through optical centre do not deviate because it strikes the surface perpendicularly and thus the angle of incidence is 0 and the angle of reflection is also 0 . And thus it reflect s back in the same media