I, like everybody I suppose, have read the explanations why the colour of the sky is blue:


  ... the two most common types of matter present in the atmosphere are
  gaseous nitrogen and oxygen. These particles are most effective in
  scattering the higher frequency and shorter wavelength portions of the
  visible light spectrum. This scattering process involves the
  absorption of a light wave by an atom followed by reemission of a
  light wave in a variety of directions. The amount of multidirectional
  scattering that occurs is dependent upon the frequency of the light.
  ... So as white light.. from the sun passes through our atmosphere,
  the high frequencies become scattered by atmospheric particles while
  the lower frequencies are most likely to pass through the atmosphere
  without a significant alteration in their direction. This scattering
  of the higher frequencies of light illuminates the skies with light on
  the BIV end of the visible spectrum. Compared to blue light, violet
  light is most easily scattered by atmospheric particles. However, our
  eyes are more sensitive to light with blue frequencies. Thus, we view
  the skies as being blue in color.


and why sunsets are red:


  ... the light that is not scattered is able to pass through our
  atmosphere and reach our eyes in a rather non-interrupted path. The
  lower frequencies of sunlight (ROY) tend to reach our eyes as we sight
  directly at the sun during midday. While sunlight consists of the
  entire range of frequencies of visible light, not all frequencies are
  equally intense. In fact, sunlight tends to be most rich with yellow
  light frequencies. For these reasons, the sun appears yellow during
  midday due to the direct passage of dominant amounts of yellow
  frequencies through our atmosphere and to our eyes.
  
  The appearance of the sun changes with the time of day. While it may
  be yellow during midday, it is often found to gradually turn color as
  it approaches sunset. This can be explained by light scattering. As
  the sun approaches the horizon line, sunlight must traverse a greater
  distance through our atmosphere; this is demonstrated in the diagram
  below. As the path that sunlight takes through our atmosphere
  increases in length, ROYGBIV encounters more and more atmospheric
  particles. This results in the scattering of greater and greater
  amounts of yellow light. During sunset hours, the light passing
  through our atmosphere to our eyes tends to be most concentrated with
  red and orange frequencies of light. For this reason, the sunsets have
  a reddish-orange hue. The effect of a red sunset becomes more
  pronounced if the atmosphere contains more and more particles.


Can you explain why the colour of the sky passes from blue to orange/red skipping altogether the whole range of green frequencies?

I have only heard of the legendary 'green, emerald line/ flash' 



that appears in particular circumstances


  Green flashes are enhanced by mirage, which increase refraction... is more likely to be seen in stable, clear air,... One might expect to see a blue flash, since blue light is
  refracted most of all, and ... is
  therefore the very last to disappear below the horizon, but the blue
  is preferentially scattered out of the line of sight, and the
  remaining light ends up appearing green


but I have never seen it, nor do I know anybody who ever did.

The sky does not skip over the green range of frequencies. The sky is green. Remove the scattered light from the Sun and the Moon and even the starlight, if you so wish, and you'll be left with something called airglow (check out the link, it's awesome, great pics, and nice explanation).

Because the link does such a good job explaining airglow, I'll skip the nitty gritty.

So you might be thinking, "Jim, you half-insane ceiling fan, everybody knows that the night sky is black!" Well, you're only half right. The night sky isn't black. The link above explains the science of it, but if that's not good enough, try to remember back to a time when you might have been out in the countryside. No bright city lights, just the night sky and trees. Now when you look at the horizon, can you see the trees? Yes, they're black silhouettes against the night sky. But how could you see black against black? The night sky isn't black. It's green thanks to airglow (or, if you're near a city, orange thanks to light pollution).

Stop, it's picture time. Here's an above the atmosphere view of the night sky from Wikipedia:



And one from the link I posted, just in case you didn't check it out:



See, don't be worried about green. The sky gets around to being green all the time.
