Your oversimplifying. No offense, but your calculation is a bit of a spherical cow in vacuum.
I am not gonna do the math, but the concept is simple: to cool a small amount of air you must heat a larger amount of air somewhere else. A/C is basically a heater overall, that consumes more “fuel” (whatever is your fuel) than normal, winter heating per identical volume of heated air.
That is why they say it is not great. Regarding the calculations, all co2 based calculations are not really accurate. It depends on the energy source, on the efficiency of energy production, on location of production, of supply chain… CO2 measures for a given product are extreme, inaccurate approximations not really meaningful on large scales. I won’t worry too much. I’d use A/C only when needed, with target temperature between 25 and 28, and you’ve done your part