The Cartesian coordinate system is a right-handed system, contrary to the initial assumption that it is left-handed. This misconception is common but not universally accepted, as some fields may use different conventions. The discussion humorously suggests that the friend's confusion may stem from their background in fields like geology or GPS, which sometimes utilize alternative coordinate systems. Overall, the conversation highlights the importance of understanding the context in which coordinate systems are applied. The Cartesian system remains predominantly recognized as right-handed in standard mathematics.