When you de-ionize something, you essentially remove everything that's not the basic molecular structure of the material. In this case, the minerals are all ionic, and you remove them leaving nothing but pure H2O molecules. Since there are no ions (minerals) the material tends to want to collect them again, and you become the sacrificial host.
Minerals in the water are what makes it taste not-flat.
I mean, what happens to the minerals in your body that you're saying it strips? It sounds like it goes into the water when you drink it, which your body then absorbs...
You pass the water as urine.
OK, so your body never gets the minerals out of water (they get lost in urine). Thus you want the water full of minerals when it enters so it won't take any more when it leaves.