For a number of reasons.
We already use dogs at airports, but we should be using a lot more of them. I know they're around but I've never been personally approached by a dog while in an airport security line. I think every air passenger should be getting some sniffs.
For one, dogs are less intrusive than the body scanners. Their use in law enforcement has already been litigated for constitutionality. They've been found to be relatively uninvasive, and their use guidelines, whatever they may be, are known. It seems to me people would be more supportive of increasing use of dogs than screening a vague picture of their naked body.
Secondly, from what I know of dogs, they're extremely effective in detecting explosives and other substances, likely much more effective than the body scanners. Terrorists know this too. I would think the high-visibility presence of dogs at security lines would be an outstanding deterrent to anyone thinking about bringing a bomb on a plane. They don't have to be mean-looking dogs, either- a lab with floppy ears and a wagging tail would detect bombs just as well as a German Shepherd. Some people might be allergic to or nervous around them, but they could always talk to security about it and find another way. With the right training for the dogs those drawbacks should be minimal anyway. Actually, in many ways the dogs might make passengers less anxious, especially with the right dogs. Between the explosives-sniffing dogs, metal detectors and luggage screening, planes could be pretty safe.
Finally, I would guess that adding two or three dogs to a security checkpoint rather than a body scanner would be cheaper and take less passenger time for security. This article says that the body scanners cost between $150K and $200K each:
http://www.globalpost.com/dispatch/european-union/100120/airport-security-body-scanner . Although dogs require extensive training (about 600 hours' worth, according to this organization:
http://www.bombdogdetection.com/bomb-dog-training.html ), I can't imagine even two or three of these dogs would cost more than $100,000. Further, walking a dog along a line of passengers already waiting for security screening would be much more time efficient than doing a full-body scan of each and every passenger.
Anyway, just my two cents on the subject.