Two comments. First, weev is known, not anonymous. That hasn't seemed to stop him, if Kathy's post can be believed.
Second, do you remember the old Smurf attack? You sent pings to a bunch of networks' broadcast address, with a forged address. So the machines on the networks replied to the pings. For one packet sent out, you could get a hundred aimed at the victim's machine. You can wind up with something like that here: If you end anonymity, then someone can forge something horrible as coming from you, and all the honest, morally upright people online will come down on you in outrage. (In her article, Kathy mentions trolls/harassers already using tactics like this.)
Second, do you remember the old Smurf attack? You sent pings to a bunch of networks' broadcast address, with a forged address. So the machines on the networks replied to the pings. For one packet sent out, you could get a hundred aimed at the victim's machine. You can wind up with something like that here: If you end anonymity, then someone can forge something horrible as coming from you, and all the honest, morally upright people online will come down on you in outrage. (In her article, Kathy mentions trolls/harassers already using tactics like this.)