Can't understand specific problem of Bitcoin anonymity There is an problem shown in bitcoinwiki:


  Someone runs both a money
  exchanger and a site meant to trap people. When Mr. Doe buys from the
  exchanger and uses those same coins to buy something from the trap
  site, the attacker can prove that these two transactions were made by
  the same person. The block chain would show:
  
  Import coins from address A. Send 100 to B. Authorized by (signature).
  
  Import coins from address B. Send 100 to C. Authorized by (signature).
  
  Bitcoin transactions do not have a "from" address, but if the attacker
  believes that address B is controlled by Mr. Doe because the attacker
  received $5 from Mr. Doe's PayPal account and then sent 100 BTC to
  that address then they can infer the identity of the party sending to
  C. This assumption is not always correct because address B may have
  been an address held on behalf of Mr. Doe by a third party and the
  transaction to C may have been unrelated.


I can't understand several issues. Is "someone who runs both a money exchanger and a site meant to trap people" attacker? If so, than I (as attacker) already know the owner of address B, don't I? why I need trap site?
I (as attacker) already know the owner of address B, don't I? why I
  need trap site?


You're right, if you sold the bitcoin and sent it to an address, and you know the identity of the person to whom it was sold (from KYC, for example), then you can associate that person that address. Since it is publicly verifiable on the blockchain, you don't need a trap site in order to see when that bitcoin is spent, but if you run a trap site, you can determine what they spent the Bitcoin on.