Some stats… Between 33 and 40 per cent of all people experience some form of anxiety when it comes to flying. And between 2.5 per cent and 5 per cent of the population have crippling anxiety, a genuine fear of flying that needs to be classified as a clinical phobia. 
Some more stats… The odds of dying in a plane crash due to a fatal accident is about 1 in 200,000. An almost zero (0.000005) per cent chance. And in fact you’re about two thousand times more likely to meet with a threatening accident on the way to the airport than you are while in the air (provided you travel by car). You’re even more likely to die because of a crazy dog who bites you than you are in an airplane. And of course you’re even more likely to kill yourself than you are to die due to a plane crash. OK, enough stats. 
So why do so many people fear traveling in the air when it’s literally the safest form of travel?
Our innate irrationality of emotions seems to be at play here.
No matter how justified airplane travel will seem to you after reading all these statistics and perhaps having already been acquainted with knowledge that airplane travel is very safe and there’s nothing to fear about it; there still will be those 33-40 per cent of people reading feeling a little anxiety the next time they sit in an airplane (I’m not saying that’s going to be inevitable but it’s sadly the most likely case).
Psychologists call this tendency of emotions recalcitrant emotions.
recalcitrant adjective - Having an obstinately uncooperative attitude towards authority or discipline.  Synonyms: uncooperative, obstinately disobedient, unmanageable.
In our case, the “authority or discipline” is the knowledge and awareness of how illogical it is to be afraid of flying. And emotion visibly tends to have an “obstinately uncooperative attitude” toward it.
That is, we get afraid in spite of the fact that there is nothing to be afraid of. And we know that there is nothing to be afraid of. But fear still dominates our thinking unyieldingly (that should hopefully make the use of the word recalcitrant clear).
Once we understand what this kind of pathological fear is, we start seeing examples of the similar kind everywhere.
More examples of irrational emotions in use
- When we’re trying to lose weight; we know what not to eat. But still when we see a cupcake lying around, we grab it, part-consciously aware that we ought not to eat it, but still we devour it because the monkey part of our mind obstinately acts disobediently to the notion of losing weight. And all the calories and logic in the world cannot make that monkey stop when instant gratification really kicks in for:
“It is easier to resist at the beginning than at the end.”Leonardo da Vinci
- When someone tells us we’re wrong; say principally wrong about something, and provides us with rationally reasonable facts about the falsity of our opinion, we still pretty often fight or flight to the situation rather than accepting the literal truth. We feel threatened. And you know what we do when we feel threatened? We act impulsively. The facts are right in front of our eyes. But we shall defend our beliefs. For although they may not be true, we care more to be respected and of our self-respect than understanding the truth. This is why we even tend to remain with our beliefs instead of making something up to win the verbal battle. We care about self-respect. If we don’t believe our outlook on life is correct, we lose that pride. So we must instead use the false belief system.
Emotions are a tricky bit. When they act in a misleading way, they can mislead you a good deal. But without them, humanity would probably not exist right now. If we’d all be entirely analytical and rational all the time in the pre-historic days in the dense Savanna Plains environment; we wouldn’t have survived! For if we encountered a lion, emotions would either put us on guard (literally—with our stone tools) or we’d run away to safety. Thanks to fear we’d probably win the lion battle. But if we didn’t feel fear, we’d be analyzing the threat, taking our time, measuring and deducing “truths” about the circumstance; and… we’d all be eaten by the king of the jungle. Perhaps some early humans did not feel fear (I’m taking a wild guess here), but luckily or not for us natural selection optimized for the lions so we survived the jungle somehow and now we don’t need to worry about getting hit by cars on the road because of being too busy analyzing the velocity approach of the vehicle. Instead we’ve got fear (which can sometimes be completely irrational).
- Fear of Flying Statistics, Trends & Facts (2021 Data) — Stratos Jet Charters
 – Odds of Dying — Injury Facts
 – Oxford Languages Dictionary: recalcitrant
Irrational Emotions and their Cognitive Impenetrability — Imperfect Cognitions