There can be no reason (that CO2 is not as good an emitter as it is an absorber of IR radiation) because the claim is false. CO2 in the atmosphere emits almost exactly the same amount and kinds of radiation as it absorbs.
But, by being both a good absorber and emitter of IR, it scatters the thermal radiation emitted by the Earth in all directions – including sending some of it back where it came from to re-warm the Earth’s surface, which slows down the radiative cooling at any given temperature (or equivalently raises the temperature required for a given cooling rate).
Of course it also does the same to IR radiation coming in from the sun, but not to the higher frequencies which are included in sunlight because the sun is so much hotter; so it’s relative effect on the Earth’s daytime warming is less than on the cooling and this slightly raises the equilibrium temperature (at which the total amount of radiation escaping from the top of the atmosphere over 24 hours exactly matches the daily total amount coming in).