Bitcoin is backed by the agreement of people that use bitcoin that it has a certain value. This value tends to change as more people use bitcoin, as there are only so many of them.
That is not backing. Backing requires responsibility. If all of the people who accept bitcoin today suddenly stop tomorrow, who will enforce their guarantee? No one has made legally binding promises to exchange Bitcoins for anything in the future.
The U.S. Dollar is similarly backed by the agreement of the people that it has a certain value. However, that value may change because an outside authority has the power to print more of such money, thus diluting what your current money is worth. Therefore, the U.S. Dollar is an investment vehicle guaranteed to lose value over time in relation to any fixed commodity.
The US Dollar is backed by two guarantees in US law, deriving from Constitution. One is that the US Government will accept them in payment for taxes. The other is that the US Government will, via its legal apparatus, allow any debts held between US citizens to be settled by US Dollars.
This is what gives the US Dollar its value. A large organisation (a government, with a big military) promises to accept them as payment. They can print more, but the rate at which they can do this is limited because they need to maintain the value of new treasury bonds. Since 1960, the rate of inflation of US Dollars has mostly stayed in the 3-5% range (two big peaks over 10%, in the mid '70s and early '80s) and so someone accepting US dollars can be fairly confident that if they spend them again in a few weeks they'll have approximately the same value and even if they keep them for a year or two without investing them they won't lose much.
In contrast, bitcoins can gain or lose 50% of their value overnight. This makes them irrelevant as a currency. How do I price my goods or services in bitcoins when the value is totally unpredictable? It's popular among speculators, because they can make a lot of money if they make good guesses, and the increasing number of speculators keeps driving the price up. If a better game comes out, the value of bitcoins will plummet. And the lower limit on their value is 0, because there is nothing backing them.
The government does not "back" the dollar at all. If you give them a dollar, they will give you nothing in return, but another dollar.
You appear not to understand the concept of backing a currency.