For the most of prehistory that is true. But for the current increase in CO2 (120 ppm and rising) to be caused by warming there would need to be 12C or so of prior warming in the last 800 years or so. That did not happen. Therefore the rise in CO2 comes from something else. The vast majority of the cause is fossil. Some from recent decreases in vegetation. A very small amount from recent increases in volcanic activity. Fossil and cement making are the simplest explanation.
You have missed the point of my post. The issue is not the origin of the CO2, but the causal relationship supposedly demonstrated by Gore’s chart. My point was that, historically, the rise in temperature was the cause of the rise in CO2. Gore had, incorrectly, asserted the reverse; i.e., that increases in CO2 had caused the temperature to rise.
The current increase in atmospheric CO2 is usually attributed to the increase in the burning of fossil fuels. This is probably true, but may also be attributed to other causes.