I also wonder if the perception that "flying is dangerous" may come about due to the sheer number of people who can die in a single plane crash (e.g. in the hundreds) whereas it's (usually) much less in a car crash
When my career started to depend on having to fly frequently, I had to overcome my fear of flying. Read a couple of really good books that were incredibly helpful. One mentioned that you rarely see coverage of a fatal car crash....but if an airplane has any trouble and footage is available they'll play it a million times. The visual imagery "locks" in your brain giving one the impression that planes crash all the time. They don't.
They also suggested not watching repeated showings of any air crashes. Just change the channel.