I am an instrument rated private pilot. What your dad told you is true but is also mostly preventable. Sometimes there are accidents that you don't know ahead of time will happen: I've had a friend who died on a local flight trying to challenge himself with strong winds in a mountainous airport, had a heart attack and died. However, that kind of accidents, equipment failure accidents are in the minority. Most accidents are pilot error. That's been studied a lot in general aviation. The conclusion is that most general aviation accidents are preventable. Pilot going into situations that a little planning and thought could prevent. [0]

As a private pilot it is mostly your choice what situation you put yourself through. To survive being a pilot you need a certain amount of humility and understanding your limitations. Also a lot of planning, including contingency plans on what to do if you get stuck somewhere or if the weather gets bad. You are not an airline, you do not have the equipment and resources they do and you should plan accordingly. This should be part of your training and it is up to you to maintain this as you fly.

If you are interested, a good book on the subject of general aviation accidents and as it relates to private pilots is The Killing Zone, Second Edition: How & Why Pilots Die by Paul Craig. Very readable book.

Additionally, aviation accidents are studied by many people in the industry and there are checklists to follow before and during the flight (IM SAFE [1], PAVE[2]. etc...) that should help you to determine if you even should make the flight. There are also automated tools that calculate based on your experience and the environmental conditions if its a go/no go [3] and if you stick to these things they would make you a very safe pilot. So I wouldn't let a fear of getting into an accident stop you from being a pilot but be smart and follow the rules, set yourself some conservative personal minimums, follow the checklists, and plan, plan, plan and you should be safe.

[0] The Nall Report, the gold standard: https://www.aopa.org/-/media/files/aopa/home/training-and-sa... [1]https://www.thebalancecareers.com/the-i-m-safe-checklist-282... [2] https://www.faa.gov/training_testing/training/fits/guidance/... [3] AOPA used to have a go/no-go decision maker can't find the link.