Everything we do, in this fallen world, has an associated health risk, which cannot be reduced to zero. (There are no utopias down here.) So all we can do is try to make choices which minimize our risk.

For example, if I go out in my car to buy groceries, there is a chance (small, but not zero) that I will get in a car accident and be killed. If I stay home and don't buy groceries, there is a larger risk that I will starve to death. So I take the smaller risk, without giving it much further thought. (Indeed, it isn't worthy of much further thought.) I know, from experience, that the risk is real but small. I judge the risk to be worth the benefit. I would judge differently if I didn't need to eat. Why risk a trip to the grocery store for nothing?

The same thing is going on with airport scanners. They, too have an associated health risk. But it is a very small risk --- probably significantly less than traffic accident injury. The general population has no feeling for this (i.e., they have virtually no real-life experience with radiation risk), so they have to rely on experts who have made it their business to learn the numbers on this. The experts tell us, pretty clearly, that health risk from these scanners is very small. They are right about this as far as objective scientific knowledge is concerned, and I can see no rational reason to doubt them. So I would personally not be in the least alarmed to be scanned by an airport scanner in preparation for a flight --- in the same sense in which I would not be in the least alarmed to hop in my car and go get groceries. Still, if I did not need to be scanned, I wouldn't.

I routinely avoid dental x-rays for myself and my family because there is a (small) cancer risk associated with all x-rays and I find that the dentist can, in fact, 99% of the time, do what needs to be done just fine without them.

Unfortunately, due to certain individuals wishing to blow up airplanes, we (American citizens) find the (very small) risk due to use of airport scanners to be unavoidable. So we use them, accepting the fact that their benefit significantly outweighs their risk.