private planes are much more dangerous, being almost as dangerous per mile as a regular car
that is because they are operated by semi-competent people who often have less practice then they have in car.
imagine how competent driver you are when you have your fresh license. it is the same with piloting license. and now imagine you are a hobby pilot and can afford to spend in the cockpit 3 hours per month. your skill is not really going to get significantly better. you are probably flying airplane that is at the end of its life, because that is only one you can afford, and there may be no one keeping an eye on you telling you "this is not how we do it, it is risky, dangerous, and you will get someone killed".