In the answer, they note that the radiation risk is minimal, but there are genuine privacy concerns:
Let's be blunt: a full-body scan means whenever you pass through airport security, you're going to have a total stranger look at you naked. Millimeter-wave scans in particular are luridly detailed. True, faces are purposely blurred, the scan inspector is in a remote locked room, never sees you in person, and isn't allowed to carry a cell phone with a camera, and the images are discarded immediately after inspection.
But remember we're dealing here with the TSA, the outfit whose agents made a nursing mother drink her own breast milk, mistook a Congressional Medal of Honor for a ninja throwing star, and forced a woman to remove her nipple rings with pliers. In March of this year a British Aviation Authority employee got a harassment warning from police after he captured an image of a female colleague passing through a full-body scanner at Heathrow airport. In May a TSA employee in Miami took a baton to a coworker who'd made fun of his genitalia after he passed through a scanner.
You may think that's a small price to pay if it means bad guys can never sneak weapons onto planes. But scans don't guarantee that. They can't detect items concealed in body cavities or by folds of flesh. "These technologies can be evaded relatively easily," a radiation safety expert tells me. "It's a money-making invasion of privacy."