There are easier "facts" to disprove AGW that don't rely on innumeracy. I mean you don't really care, you just want to have a "gotcha" and not think past that, but AGW was considered disproved for a few decades and you could get some "stumpers" that aren't quite as silly as playing number games.

The oceans can absorb a practically infinite amount of CO2, so there's no way for it to build up in the atmosphere in the long run. Also, the atmosphere is already saturated with CO2 to the point where adding more will have no effect. Also, water vapor's absorption spectrum overlaps that of CO2 so there is no way for CO2 to have any additional effect. All of these facts were known more than a century ago, and consequently AGW was considered disproved.

"Skeptics" should not read past this point, because it turns out all of those things are misleading. The oceans don't mix fast enough to prevent CO2 buildup, and the action of CO2 is felt not in the lower atmosphere but at the radiative top-of-atmosphere, the point where outgoing infrared radiation is more likely to escape to space than strike another molecule. Adding CO2 makes the CO2-dense region greater in extent, thus the outgoing heat takes longer to leave Earth, thus raising the total atmosphere temperature and causing a nasty feedback mechanism with H2O. Because this changes which elevation energy gets radiated at, we can directly measure it. Checkmate skeptics.

To tie this back in to the main point, Callendar was one of the prime movers in rehabilitating the AGW theory (one of his papers amusingly refers to the theory's "checkered past"), but it took until Keeling's work in the late 1950s to conclusively demonstrate the year-over-year increase in atmospheric CO2 concentrations.