confession: I don't like it either. (would actually rather go thirsty) I will try it again, next water fast. But I drink spring water. we do the best we can...
For me, the issue is likely the plastic, since I don't own a distiller, and only plastic has been available to me, up to now. I have read that adding a few grains of brown rice to a carafe of distilled water will shift it away from that vacuum of 'nothingness' and into something that tastes less dead. It's the minute amounts of minerals that does it.
I find it tastes "dry", or rather, like plastic, not tastewise, but in terms of wetness, or something. It's a strange beast I have yet to grasp. :-)
but I vaguely remember the taste of fresh rain, decades ago, when it tasted clean and washed, rather than loaded with poisons. And it was good! More like dew. That's "Natural" distilled water. The other kind is all manufactured.