Greenhouse gases
Let's look a bit closer at the claims of Doug Cotton, and of Claes Johnson, whose work Doug relies upon. It's important because this is one of the strongest claims made by those who choose to reject the notion of anthropogenic climate change.
Here's the core claim, from Doug Coton:
The assumption is made that so-called "backradiation" from a cold atmosphere is able to transfer thermal energy to a surface which is warmer than the source of the radiation. This is a physical impossibility as is proven theoretically by Prof Claes Johnson and empirically by Prof. Nasif Nahle
The claim, contradictory to over a century of thermodynamics, is that a body will only radiate heat towards bodies colder than it, and never towards bodies hotter than it. Note that this is not a claim about net heat transfer, but about any radiated heat.
Apparently, this happens through the following mechanism according to Professor Claes Johnson:
[a body] reads the temperature of the surrounding from its spectrum, and then decides to cool or warm depending on its own temperature
The Johnson/Cotton theory is that almost everyone other than them misinterprets the Stefan-Boltzmann Law, and that there is no such thing as photons of infra-red radiation.
And the problem with all of this is that this is an extraordinary claim that lacks any evidence at all. Thermodynamics, the theory of photons, and of black-body radiation, have all made astonishingly successful predictions, and are supported by many decades of empirical evidence.
The article you quoted frankly reads very poorly. It quotes a lot of stuff without once noting that greenhouse effects absolutely are real and critical to the earth being habitable. I don't know who this fellow is, but if he posted here directly I'd give it an instant negative vote.
You, sir, I'm giving a thumbs up for taking the trouble to ask in a forum where you are likely to get some answers. More people should do that when they hear odd science claims!
Now, with that said, it's absolutely true that both carbon dioxide and methane are bit players in the overall greenhouse effect.
The main greenhouse is water vapor, by about two orders of magnitude. My recollection without looking it up is that 97 to 98 percent of the greenhouse effect is caused by water vapor. This is why it gets so cold in the desert at night, for example.
The Nobel-prize winning models for global warming do not invoke direct warming from carbon dioxide. Instead, they postulate and model using computer programs the idea that the very small additive impacts of carbon dioxide, methane, and other minor greenhouse gases throw off the balance of the major player, water vapor. I do not know how they do that part of the model. It has to be complicated, since water vapor levels vary with near-fractal complexity from day to day and from region to region.