I have several friends and colleagues who suffer from fear of flying and have run seminars to try to help them.
It is, like most phobias, irrational. Explaining what keeps the 'plane aloft does not really solve the problem, nor does explaining the various noises and movements which take place during a flight. The conversations always turns to the 'what if ....' type questions. Interestingly, in my experience, most people find turbulence scarier than anything else.
Unfortunately most of that 'what ifs' are based on actual accidents, so it is hard to deny that they happen, one can only say that the chances are negligible and that the investigations after each event make flying safer. It doesn't help!
One of our friends has a phobia about dogs, and our gentle soppy labrador/beagle had to be locked up when he came round. Nothing would persuade him that the dog was not going to tear out his throat!