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You seem to be ignoring the green-house system in your argument. The idea is that IR energy (that enters the system at a higher state), is not reradiated into space, and is intercepted by atmospheric CO2 because of its opacity to long-wave radiation. As the concentration of CO2 increases, the overall interception rate goes up. That heat can then be reradiated into the surrounding atmosphere.

The reason why CO2 is neutral as far as IR radiation is concerned is already explained in my previous posts. CO2 does not care from which direction the IR originates, nor does it reradiate it directionally. Therefore, it does not act as a mirror to reflect the IR radiation back to earth. Since its fluorescence activity occurs within the IR band, it converts no visible light to IR light, and therefore has less of an effect on temperature than any of the many materials that absorb visible light and reradiate some of it as IR light.