The rebuttal would be that the dollar could also be worth 50% less the next day.
That is a lot less likely to happen to the dollar then with bitcoins..
What are you comparing the Dollar to in this assumption, because when people say "bitcoins could drop in value by half tommorrow" the common assumption is that is compared to US $. If the reverse comparison is also true, then the dollar has already drop significantly over the past couple of months alone, and by orders of magnitude over the past three years.