One argument that you can use is that drinking softened water can be a health concern. The softening process removes calcium and magnesium ions from the water and replaces them with sodium ions. Calcium and magnesium in hard water are not a health treat. Sodium ions, however, may have negative consequences on cardiac health. Hopefully, your water system has a bypass that allows tap drinking water that doesn't come from the water softener. Or you're concerned about the quality of your tap water, perhaps you should drink bottled spring water.

But, perhaps more importantly, do you really want to drink primarily distilled water? Is it healthy? In my opinion, the answer is no. Magnesium, calcium, and other trace minerals in undistilled water are good for you. These minerals are removed by distillation. Plaque in veins does not come from these minerals. Plaque in pipes is from insoluble inorganic salt deposits made from calcium and maganesium. However, plaque in veins is something entirely different; it is organic and does not come from metal ions. Here's a link from Mercola's website which makes the argument that drinking distilled water is NOT good for you:

Why I Say No to Distilled Water Only