The teacher says that because the wavelength of blue light is less than red light the sky appears blue during a clear day; but why not violet or indigo; because their wavelengths are even lesser than than that of red and  blue.

The reason is that the human eye has much lower response to violet and indigo colour as compared to blue colour. The sensitivity of the human eye is very wavelength dependent, and is more sensitive to blue light.

Also, the fact that the energy contained in the violet spectrum is much smaller then contained in the blue spectrum.

Thus, the sky appears blue and not violet or indigo.