How is it any different than the government printing dollars which make the claim that they are legal tender? Should you just take their word for it? You have a piece of paper in your pocket that you can exchange for quite a bit of food, but the paper isn't valuable. It's not magic paper, it can't cure hemorrhoids. It's just paper, with little pieces of thread and stuff. It would take several thousand pieces of it to equal the value of 1 log of firewood.
Like anything else, be it little pieces of paper or metal, or hashes and algorithms, or bottle caps, barbie doll heads, marbles, whatever; the true value of something is exactly what someone is willing to pay for it. The prices on the exchanges are actual prices, that is what people are actually willing to pay. That is what a bitcoin is actually worth. Just like dollars and coins.
That being said, a lot of time needs to pass before anyone should seriously consider converting the majority of their wealth to a currency like bitcoins. If the US dollar or any other state-sponsored currency were seeing volatility like what you see with BTC then no one would be keeping their fortune there, either. The reason USD is a better currency at this point to store your money is because right now it is much more stable than BTC. That's really the only reason though.