Does climate change cause increase in CO2? My main question is how do we know that increase in global temperature does not CAUSE an increase in CO2 concentration?

I am trying to develop my mental model of what's going on for the climate change issue.  There is definitely a correlation between global temperature and CO2 concentration, this is not disputed.  The general consensus is that CO2 increase causes temperature increase, why is the reverse situation not studied (if it is I could not find any studies).

This thought comes from the statement I've seen that water vapor concentration is more correlated to global temperature  than CO2, but this is intuitive since warmer air holds more water vapor than colder air.  Does the same intuition hold for CO2?

I am not an expert on the subject; so I understand that I may be way off base with my reasoning.  I also openly accept  edits to my question if it is not structured or presented properly.
One reason is that we know exactly where the current increased CO2 comes from.  That is, we know from economic data how much petroleum, natural gas, &amp; coal is extracted and burned.  From that simple chemistry lets us compute the amount of CO2 produced, and we find that (after allowing for factors such as e.g. some being absorbed by the oceans) that the amount created by burning fossil fuels matches the observed increase.

(There are also more subtle measurements, such as isotope ratios, which I'm not qualified to expound in any detail...)

Another reason is that for warming to have caused the observed increase in CO2, there'd have to be some other cause for the warming.  No such cause has been found.  Suggested causes such as variation in solar output have been ruled out by measurements.