How are CO2 and O2 levels regulated in a planted aquarium? Many answers involve CO2 injection but why?

I am wondering from a Chemistry stand point why aeration/turbulent water is sufficient to provide atmospheric oxygen exchange for aquatic animals, but why it is not sufficient to provide CO2 for aquatic plants? Why must the water actually be injected with CO2, and aeration actually results in the loss of CO2 from the system? Isn't CO2 more soluble in water than O2? I am not arguing that it isn't necessary, just want to know why. Are plants using CO2 faster than aquatic animals use O2?