When atmospheric CO₂ increases, the stratosphere cools. This cooling is one of the most robust signals of CO₂-induced climate change, yet several fundamental questions about stratospheric cooling remain unanswered. Here we explain that stratospheric cooling emerges because rising CO₂ levels increase the number of frequencies in the CO₂ band which can effectively emit infrared radiation to space. These mechanisms explain the magnitude and vertical structure of stratospheric cooling and clarify why stratospheric cooling amplifies the energy imbalance that CO₂ induces at the top of the atmosphere by about 75%.