It is absolutely true that breathing is commanded by CO2. Exactly for this reason a proper breathing technique can improve the situation significantly. If you leave the CO2 to command your breathing, you easily go in Dyspnea: this is an anomalous breathing mode, where a lot of CO2 is accumulated in your body, stimulating breathing. But the "natural way" of reacting to such a stimulus is to speed up the breathing rate, not to increase the volume of each respiration. The result is a very fast, very shallow breathing, which is highly inefficient in removing the CO2. So a vicious circle is established, the more CO2 you have, the faster is the breathing.
The correct way of breathing for not retenting CO2 is the way which is taught for CC rebreathers, particularly those operating with a single hose (as the old ARO pure-oxygen rebreathers which were widely employed, here in Italy, in the seventies and eighties).
With such rebreathers you are obliged to breath very slowly, always depleting your lungs almost entirely, very, very slowly, and filling them up almost completely, again very slowly. An inspiratory pause of 5-10s further improves the efficiency of CO2 elimination, as when the lungs are fully extended the exchange surface is maximum, so CO2 is expelled better form the blood.
Learning this way of breathing takes months. In fact, in the seventies, a scuba diving course was 6-9 months long, during which the ARO was employed routinely, mostly in the swimming pool, whilst OC air was employed only in the last lessons and in the sea.
All this was entirely incompatible with the PADI method, based on a very quick and superficial OW training, followed by a large number of other "speciality" courses.
Teaching breathing control, in this approach, is not only too slow and too difficult, it is also quite dangerous: in particular the inspiratory pause, or the simple fact of reaching full inhalation, increases significantly the chance that a student emerges quickly without exhaling, causing severe lung damage and gas embolism.
Better to tell him to just "breath normally", and leave that he gets a bad headache due to CO2 retention for not being able to eliminate it efficiently with proper breathing control, than risking much worst physical damage due to a quick uncontrolled ascent without expiration...