electromagnetic radiation - If both radio waves and gamma rays can travel through walls

and they are on opposite ends of the electromagnetic spectrum, then why can't light travel through walls which is right in the middle of the spectrum?

This question has already been asked here. However, I am not entirely satisfied by the answer given on that page which relies on fanciful analogies and metaphors of ants, elephants etc. I am looking for a better explanation.

I think the crux of the matter, and my dilemma, relates to formula for penetration depth. This is a well known formula used to explain the fact that low frequency waves have more penetration than high frequency waves.

But then how come gamma waves have such high penetration?

Are there some assumptions behind derivation of this formula which break when we consider very high frequency waves?

Or, are there some new factors that need to be taken into account as we move into the high frequency regime?

If given a radio source and a gamma source of equal intensity, then will the radio source have more penetrability than the gamma source per formula for penetration depth? If not, why not?

Thanks for all those who posted answers to this question. The answer being proposed is that light waves have the right energy to interact with atoms and electrons in the matter and thus get absorbed. This is a quantum mechanical explanation. The skin depth, on the other hand, is derived purely on basis of classical electrodynamics. So I see there are two mechanisms at work here? Does anyone agree with this? If so, the net absorption will be the sum of absorption due to skin effect + absorption due to atomic physics. Now if we take gamma rays - agreed there will be no absorption due to atomic physics but there should be absorption in accordance with skin effect. And so I come back to original problem.