What the hell!? You think electronic fiat transactions are more anonymous than bitcoins? With bitcoins you can mix your coins, how the hell do you do that with fiat? Run a shady drug ring out of your backyard!? Come on man. That doesn't make sense at all.
"mixing bitcoin" is a somewhat clumsy way to obtain a kind of anonymity in bitcoin, but you need a third, trusted party for that, and (shady ?) partners that want to mix too. With sufficient effort, such "mixing constructions" can be obtained with fiat too if you are allowed to trust third parties. The bitcoin protocol IN ITSELF doesn't allow any form of automatic anonymity.
The point is that mixing is clumsy in bitcoin, that most coins aren't mixed, that the mixing itself "colours" the coins, and that non-mixed coins, with the network of change addresses and combinations to arrive at the right amounts of payment, are propagating real-world knowledge to *anyone*, not just to banks and law enforcement if they obtain a warrant for it.
If I'm a plumber, and I get paid in bitcoin to repair the toilets in Joe's bar, and then I give some of those coins to Mary, who is my friend, and Mary goes and has a coffee at Joe's bar, then Joe can EASILY find out that the money he gave me to pay for his toilet repair, ended up in Mary's hands, so that there is a link between me and Mary. If the same is done with fiat, Joe doesn't know such a thing. Bitcoin's ledger is propagating real world knowledge like a bush fire.
Yes, I can mix my coins. Yes, I can do 20 transactions between my own accounts and pay a lot of fees to "hide" this. Joe will nevertheless see that Mary got the bitcoins he gave me at a certain point, even though now Mary COULD also have obtained them from a shady drugs dealer on the other side of the world I happened to mix with. But what should have remained (innocent) private information, is shouted out to the world with bitcoin's transparent ledger, and to even try to hide it takes me a lot of effort, and the necessity to trust a third (mixing) party ; while with fiat, that kind of innocent privacy comes automatically. If Joe has paid me with a wire transfer, and I gave money to Mary with a wire transfer, and she paid with her VISA card at the bar, then Joe cannot know in the most remote way that the money he got from her was the money he paid me. Actually, in fiat, that doesn't even make sense, because bank money is fungible while bitcoin isn't (by definition, every coin has a whole history to it which distinguishes it from another one - apart from a mixer operation).