If organic chemistry is the study of carbon, then why isn't carbon dioxide considered to be an organic compound? The answer is because organic molecules don't just contain carbon. They contain hydrocarbons or carbon bonded to hydrogen. The C-H bond has lower bond energy than the carbon-oxygen bond in carbon dioxide, making carbon dioxide (CO2) more stable/less reactive than the typical organic compound. So, when you're determining whether a carbon compound is organic or not, look to see whether it contains hydrogen in addition to carbon and whether the carbon is bonded to the hydrogen.
Past Methods of Distinguishing Between Organic and Inorganic
Although carbon dioxide contains carbon and has covalent bonds, it also fails the older test for whether or not a compound could be considered organic: Could a compound be produced from inorganic sources? Carbon dioxide occurs naturally from processes that are definitely not organic. It is released from volcanoes, minerals, and other inanimate sources. This definition of "organic" fell apart when chemists started to synthesize organic compounds from inorganic sources. For example, Wohler made urea (an organic) from ammonium chloride and potassium cyanate. In the case of carbon dioxide, yes, living organisms produce it, but so do many other natural processes. Thus, it was classified as inorganic.
Other Examples of Inorganic Carbon Molecules
Carbon dioxide isn't the only compound that contains carbon but isn't organic. Other examples include carbon monoxide (CO), sodium bicarbonate, iron cyanide complexes, and carbon tetrachloride. As you might expect, elemental carbon isn't organic either. Amorphous carbon, buckminsterfullerene, graphite, and diamond are all inorganic.