 Why was the girl unable to help Joe commit his planned crime?
When she handed the card back, Joe fought an impulse to tear it to pieces. I've been a garbage man, street-cleaner, ditch-digger—" On the other side of the room, the jukebox came to life with a roar and a group of teen-agers scrambled to the dance floor. Feeling safe from hidden microphones because of the uproar, he leaned across the table and whispered in the girl's ear, "That's what I want to hire you for. A civilization weary of murder, robbery, kidnapping, counterfeiting, blackmail, rape, arson, and drunkenness had originated the CPA—Crime Prevention Association. There were no longer any prisons—CPA officials had declared loudly and emphatically that their job was to prevent crime, not punish it. They had made crime almost impossible, and during the previous year, only a few hundred men in the whole country had been convicted of criminal acts. Instead, he was sent to a hospital where all criminal tendencies were removed from his mind by psychologists, shock treatments, encephalographic devices, a form of prefrontal lobotomy and a dozen other methods. The CPA system was, actually, cheaper than previous methods because it did away with the damage caused by countless crimes; did away with prisons and their guards, large police forces, squad cars and weapons. He was a hero to the millions of men and women who had suppressed impulses to kill someone, beat their mates, get drunk, or kick a dog. And therefore, an EX (a convicted criminal who received the treatment was commonly called an Ex because he was in the strictest sense of the word an Ex-criminal) ... The girl followed him across the room, around tables, through a door, down a hall, through a back door and into the alley. A crime because it theoretically inflicted psychological injury upon the intended victim—and because millions of women voters had voted it a crime. On the other hand, attempted murder, robbery, kidnapping, etc., were not crimes. They weren't crimes because the DCT didn't complete the act, and if he didn't complete the act, that meant simply that the CPA had once again functioned properly. Joe discovered to his dismay that the girl was telling the truth when she said she was a sergeant in the WSDA. And if the conspirators were prevented from committing a crime, then that meant the CPA had functioned properly once again. And, in slightly smaller print, the ID card stated that the owner was a DCT First Class.
 She was a part of the WSDA and obviously knew how to defend herself.
 She was a part of the CPA and didn't agree with his idea.  She was unable to accept his small payment for a large possible consequence.  She was a part of the WSDA and obviously knew how to defend herself.  She knew no one would believe that he had actually tried to rape her because of her status as a DCT.