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Does a blanket keep you warm?
Maybe you should just go naked in the winter. Afterall, your contention is the same pscience that would contend your clothes and coat aren't holding in any heat.
The old 'Magick Blanket' argument again. *sigh*
This is a false equivalence fallacy.
It is not possible to trap or retain heat. Blankets and coats work by reducing heat, not trapping it. Your body is burning food to produce thermal energy. A coat or a blanket allows your body to not lose that energy as fast, which means you can maintain your own body temperature. The heat loss doesn't overcome your own ability to produce thermal energy.
Putting a blanket on a rock will not make the rock warmer. The Earth is not producing thermal energy like you do. What the Earth IS producing (within its own interior) ALREADY has a pretty effective blanket, called solid rock, which turns out to be a pretty effective insulator.
CO2 actually conducts thermal energy better than almost any other gas in the atmosphere. It is not an insulator. It is also a gas, and part of the atmosphere. It participates in convective heating (allowing the surface to cool by heating the atmosphere and dissipating its energy over a wider area).
ALL of it radiates, the surface (most of it), the atmosphere, everything. ALL of it is radiating into space. Neither CO2 nor water inhibit that in any way. No gas inhibits that in any way.
CO2 (and water) does absorb certain frequencies of infrared light. Absorption is not warming the Earth. It is just another way for the surface to cool itself by heating the atmosphere. All it means is that instead of the surface radiating that energy away, the atmosphere does instead.
The Magick Blanket argument attempts to create a one-way insulation around the Earth. It violates the 2nd law of thermodynamics by decreasing entropy. It violates the 1st law of thermodynamics by assuming energy is created out of a non-energy source.
There is no Magick Blanket in the atmosphere. Neither CO2 nor water have the capability to trap thermal energy. It is not possible to trap heat. It is not possible to trap thermal energy. There is always heat.