Based on the fact that calcium carbonate is an ionic compound, why is it insoluble in water????
Look up your solubility rules. I'm not really sure why, but I know my book states right off that Most sulfide, carbonate, and phosphate salts are only slightly soluble. Slightly meaning that such a tiny amoutn dissolves that it's not possible to detect with the naked eye.
The lattice energy of CaCO3 is too high for the solvation energy with water molecules to break it up.