I see no difference in principle between a search using someone's hands and search using X-rays. If one objects to rights violation during a pat-down, why doesn't the same objection apply to backscatter?

A backscatter machine in some ways is even more intrusive than a pat down as it can generate higher resolution images, which can be saved. Furthermore, there is a small, but non-zero risk of bodily harm from the scan -particularly when you multiply the risk by the number of trips and passengers going through the procedure, even a one in a million chance would cause harm far in excess of the risk of terrorist threat that the search is trying to mitigate.