Why is the index of refraction always greater than or equal to 1?

The reason is because the definition of refractive index, n of a medium (eg. glass) is the ratio of the speed of light in a vacuum, c, to the speed of light in the medium, v. i.e. n=c/v

Nothing can exceed the speed of light in a vacuum. Therefore, the maximum value of n is 1, which is the refractive index of a vacuum or air (for which the refractive index is about the same as for a vacuum). When a light ray enters a medium from air or a vacuum, the speed must decrease because v < c and so n <1 because n=c/v.