Why carbonic acid is inorganic compound?

Oh, dude, carbonic acid is considered an inorganic compound because it doesn't contain carbon-hydrogen bonds, which are the hallmark of organic compounds. It's like the cool kid sitting at the inorganic chemistry table, while all the organic compounds are having their carbon-hydrogen bond party on the other side of the cafeteria. So yeah, carbonic acid is just chilling in the inorganic club, sipping its non-organic beverage.