Yeah, uh, you kind of miss the point here. Rothbard, "Fractional-Reserve Banking" and "Anatomy of the Bank Run", game over, you lose.
The problem with FRB: it constitutes fraud. While I maintain that this statement is prima-facie obvious, I have the feeling that it will escape some portion of the crowd, so we'll try a thought-experiment.
"Fractional reserve" banking says that for every, say, $1000 of demand deposits (ex. checking accounts), the bank need only keep some fraction available at any time, on the theory that not all $1000 will be demanded at once. Yes, that's sort-of true - statistically, most of the time, most people will be content to leave it in the bank, and only call it out as-needed. Most of these calls for money will, in turn, be deposited in another bank, thereby adding an extra level of "protection": inter-bank transfers can be "batched" and resolved on different time scales than the demand-deposit processing (e.g. accounts squared at end-of-day, end-of-week, whatever).
However, what the bank is saying when you deposit money in a demand-deposit account - "your money is available for withdrawal at any time of your choosing" - is, literally, not true. *Your* money has disappeared into someone else's pocket, in that it has been loaned out to some other party as soon as it hits the bank. This is not a "theoretical" untruth - it is a real untruth, in that at all times, the bank is illiquid, i.e. does not possess sufficient capital to redeem all its demand-deposit accounts on actual demand. This is what is referred to in any other instance as "constructive fraud". It is useful to compare this to the eponymous Ponzi scheme, where the fraud consists of there being no actual capital or investment to satisfy the promised payout schedule to current investors, requiring that new investors be found to service existing obligations.
This is not the worst feature of fractional-reserve banking, though. FRB is the gateway for the money multiplier and hence inflation; a bank with a reserve requirement of 5% (larger than the current reserve requirements, note; I believe they're hovering at less than 1%) can, with a deposit of $1000, immediately turn around and loan out $950 of that money. This functionally doubles the amount of money in the economy ($1000 of "fantasy" money, and $950 of "actual" money floating around). That $950 typically gets deposited in *another* fractional-reserve bank, almost invariably with the same reserve ratio (set by the central bank, and reinforced by consumer preferences; ceteris paribus, a higher reserve ratio implies lower interest rates on deposits, providing customers incentive to move their deposits to another bank), at which point the cycle starts again ($950 in "fantasy" money, of which $47.50 is kept on-hand, and the remaining $902.50 lent out). This multiplies that original $1000 of "real" money to something like $20,000 in terms of its real economic effect. SUPRISE INFLATIONSECKS LOL. Then, when you start printing up more money (cue the Fed) and tweaking reserve ratios (cue the Fed again), you wind up with - wait for it - more inflation. Inflation has well-known and universally-observed destructive effects, penalizing saving and encouraging increasing amounts of debt, since debt is paid off with future money that is worth less than the original loan. How's that working out for us so far?
(Side note: it is instructive to note the identity between fiat currency and counterfeit, with the only difference being the identity of the printer of money.)
Austrian economic theory consists of the "duh no-shit" observation that this has an effect on the economy - inflation makes money cheaper to obtain (hey, they print it for nothing!), thereby making marginal enterprises "profitable" under inflationary conditions. This produces the "boom". When those conditions cease - there is an lower bound on the worthlessness of fiat currency, beyond which it is not used except as kindling - all of those bad ideas *come home to roost*, with the accompanying cascade of economic destruction (bankruptcies, business failures, &c.) This is the "bust". The Austrian position is that a commodity that is relatively scarce and immune to counterfeit is a desired currency and is in fact *chosen* as currency when people are permitted to do so without interference. Gold fits this bill nicely. Silver does okay too. PGMs, likewise. When this system is manipulated, as it has been repeatedly in the past, the result is the boom-bust business cycle that people love so very much. The idea that it might perhaps be better to avoid the "scientific" management of human affairs - which efforts make liberal use of deceit and coercion, and which in the long run tend to produce a polity of slaves, or pyramids of human skulls, or both - is not in vogue, and has not been for some time.
Resist the temptation to believe in wise wizards who have your best interests at heart and who have things "under control". They don't.