The reason for using CO2 os probably its low critical pressure (ie, relatively easy to "liquefy"). Lots of gases will probably do but CO2 is the easiest to work with for supercritical extraction.
Liquid CO2 has solvent properties that N2 and oxygen do not have.  For example, liquid CO2 is used in industry to extract caffein from coffee beans.  This is the so-called "natural" process of decaffination.

Actually, it is not exactly correct to classify the CO2 used in petroleum wells as "liquid".  It would be more correct to call it a supercritical fluid.