> How did it get value to begin with?
It never had value. It had a price. The price of silver in 1980 was $33 an ounce, by 1981 it was under $10 an ounce. Pets.com had a market cap of $220 million in early 2000, by November it was bankrupt. Subprime mortgages, Dutch tulip bulbs, history is replete with prices temporarily overshooting their values. The difference between Bitcoin and silver, or Bitcoin and underwater real estate, is that Bitcoin is a useless hash, whereas silver and real estate have some value.
> All fiat currencies
The discussion of the price and value of fiat currencies is too complex to really cover completely in an HN comment.
The question about fiat currency also doesn't mean too much for Bitcoins. The argument seems to be "it doesn't seem to make much sense that this piece of paper is worth anything, but since it is, that means that Bitcoin is worth something". I'm not really sure how that follows. If it did make sense, it would also make sense for Dogecoin and Stellar and Litecoin and Ripple to have million dollar market caps, which in fact, they all do (technically any how).
Technically, dollars had no value even before 1971 when you could exchange them for gold. They weren't gold, they were just papers one could exchange for gold. They were an abstraction of gold.
After 1971, the US closed the window on the 10,000 tons of gold it stores at Fort Knox and elsewhere. At this point the dollar becomes an abstraction of an abstraction.
A simple announcement from the president that the gold window is open again would always put a floor under the dollar. It's the reason the US spends so much to store 10,000 tons of gold. If not, why does the US store all that gold? Wouldn't it make sense to liquidate it and pay down US debt? Fort Knox et al store that gold to give value to the dollar.