Why do Coffee machines say do not use distilled water?

To ensure optimum taste of your brewed cup. Distilled water also speeds up corrosion of heating elements, boiler walls, rubber washers etc, thus reducing their life span.

For a superior quality extraction of coffee solids, the brewing water should have these characteristics, as per standards determined by SCA - Specialty Coffee Association of America:

If interested in further reading on optimum water quality for brewing coffee, you can download SCA’s water standards handbook from here:

http://www.scaa.org/PDF/resources/water-standards.pdf