Because I need 10mg or 20mg doses. Have you ever tried to divide a tablet into 10 or 20 equal parts? If I just try to mix it in water, each ml won't be consistent in dosage because it won't form a uniform suspension. It will just be particles floating (or sinking) around in the water.
I would look up the actual drug. The insoluble stuff in the water is probably the binding agents of the tablet.
We demonstrate this for general chemistry students during a lab with Vitamin C. They need to find out how much is in a tablet, but the tablets never fully dissolve because of the binders, but the Vitamin C in the tablet easily dissolves if the tablet is broken up with a mortar and pestle first.
Edit:
Quick look online suggests that the drug has a low solubility in water (<1mg/ml). If you do need to use acid to dissolve it, I would consider doing a wet-crush of the tablet in a 1-2M solution and then diluting it appropriately to a larger volume.
Apparently, it is also soluble in warm ethanol (~20mg/ml).