It's a question of definition -- "organic" carbon compounds are those that form molecules classifed as hydrocarbons — a large family of molecules that are composed of hydrogen atoms bonded to a chain of carbon atoms. Chain length, side chains and functional groups all affect the properties of organic molecules. Many organic compounds also contain N, S, O, P and even some metals.
However, carbon-containing compounds which are associated with minerals (or which do not contain hydrogen), are treated separately from classical organic compounds. Among these are the simple oxides of carbon. The most prominent oxide is carbon dioxide (CO2) and, in minerals, metal carbonates (compounds containing the ion CO3).
So, chemists choose to separate carbon containing compounds into these two (simplistic) categories -- however the definition is not rigid.