Now ever scientific text I have ever read says that when you increase the emissivity of a thing, that thing cools more efficiently...never once have I read that increasing the emissivity of a thing helps it warm, or causes any sort of warming...
I accused you of selective vision. If a coin flip comes up heads, you point and cheer 'I win!'. If it comes up tails you say 'What coin? I don't see any coin'.
This is a perfect example. You have no problem accepting the fact that CO2 radiates energy to space at high altitude but you refuse to acknowledge that CO2 absorbs energy near the surface.
The surface is a near blackbody. It absorbs most wavelengths of radiation. But it can only emit wavelengths that can be produced according to its temperature, a wide range of IR.
The atmosphere is not even close to being a blackbody. Its emmisivity is limited to certain bands of radiation. Some wavelengths are strongly absorbed, some wavelengths do not interact. The emmisivity must be calculated on a wavelength by wavelength basis.
We can choose three representative wavelengths. 15 microns for CO2, 10 microns for direct escape to space, and 7 microns for water vapour.
At 15 microns all surface radiation is absorbed and only a fraction is lost to space and the rest returns to the surface. At 10 microns all surface radiation escapes directly to space. At 7 microns only a fraction escapes and the rest returns to the surface.
The energy returning to the surface does not 'keep' its wavelength, it is divided up into the same proportions of 15, 10, and 7 microns. Every loop through the system loses all the 10 micron radiation and only a fraction of the 15 and 7 micron radiation. Most of the energy loss is in the 10 micron band.
Do I really need to show the satellite data which show that 10 micron radiation leaves the Earth system at the surface temperature, and that 15 and 7 micron radiation leaves at a higher and cooler temperature?
Only radiation that actually leaves the Earth system can cause cooling. Simply moving energy from one location to another, from one form to another, does not cause cooling.
SSDD, you say absorption and emission do not cause warming. Okay, whatever. But the important point is that it doesn't cause cooling if the emission doesn't escape to space. You are just hiding the energy in a spot that you don't see or acknowledge.