It seems arbitrary, because it is! The general way to classify organic and inorganic compounds are by the definitions themselves. If the compound has carbon and hydrogen and occur naturally, it is an organic compound. The other compounds that are synthesized or man-made, it is called as inorganic compounds.
Diamond is made of Carbon, yet it’s not classified as an ‘organic compound’.
Diamond is an allotrope. Means, it is just Carbon existing in another form. So it is basically just Carbon, a substance.
