I doubt your math is wrong; CO2 is a small constituent of the total atmosphere.
But CO2 is the constituent in the atmosphere with an important property; it is the most prevalent atmospheric gas for which a change in its concentration will affect Earth's radiative balance. So despite the fact that there is a lot less CO2 than N2 or O2, that concentration is a very important variable in the climate system. Always has been and always will be.
How? Models that show an increase in water vapor coming from the increase in CO2. The slight (very slight relative to other gases) warming from CO2 allows the atmosphere to hold more water vapor. This much more potent GH gas then causes further warming. The problem with those models is the assumption that clouds can be described with a single parameter ignoring or trivializing the effect that the increased water vapor has on the weather.
So to say that CO2 changes the radiative balance contains several assumptions and a huge simplification that doesn't bear out in reality. Again today there are lenticular clouds leftover from overnight convection. Those affect the temperature and climate. They do not have to be modeled accurately for my particular area, but they must be modeled somehow since water vapor will create more convection and more of those effects (clouds near the top of the troposphere). But they are not modeled except in aggregate and ultimately arbitrary parameters.