Perceptions of risk in human activities

I teach this concept to my psychology students. There are two things going on here: the availability bias and something called dread risk . We tend to fear more what we are more exposed to (i.e., more available in memory), regardless of the statistics or actual risk. The dead risk is a risk with a powerful emotional component, such as a terrorist attack.

To your example, "fear" is not a rational response; it is an emotional one (we can call it "arational"). If we say that it is reasonable to fear negative events in proportion to their chance of occurring, then we call these irrational responses. But it might not be fair to judge someone's reasoning on emotional or arational grounds, since these our not fully within our cognitive control. A good example of this is how many former theists (now atheists) still have a residual fear of Hell. So fallacy? I would say no.

I think the fear is falling out of the sky, something which a car isn't likely to do. I don't much like flying, and it's nothing to do with statistics. 

It's like when I had to do abseiling or whatever it was. I understand that people use these harnesses safely but it didn't feel like it could possibly hold me, and I was unable to release my hold from the rope above the mechanism, instead lowering myself by hand. I'm sure the statistics would indicate a mangled hand was more likely, but they were irrelevant to the primal fear. 

"Surely, this is irrational...right?"

Yes, it's certainly that. As I understand it, this is a primall brain function which developed long before the frontal cortex which allows rationalisation. Just like dark corners can give me the creeps for no rational reason, which is an impulse which allowed my ancestors to survive. 

I would imagine that many people would say that their fear of flying isn't at all rational, and the ones who don't say that are simply ignorant 

This could be a little bit of a faulty comparison fallacy, since plane crashes almost always result in instant death. Whereas there are many varying degrees of car crashes. Most car crashes are not fatal (and we've all been in one to one degree or another), while most plane crashes are fatal (and most the time we've never experienced one because if we did we probably wouldn't be here to talk about it.)