Why private planes crash?
The majority of general aviation accidents come down to pilot error. This includes any crash in which the pilot loses control of the aircraft and can't regain it.
The United States has the largest and most diverse general aviation (GA) community in the world, with more than 220,000 active aircraft, including amateur-built aircraft, rotorcraft, balloons, and highly sophisticated turbojets. – Federal Aviation Administration
Where do accidents occur?
Top Causes of Fatal Accidents

The Top 10 Leading Causes of Fatal General Aviation Accidents 2001-2016:

1. Loss of Control Inflight

2. Controlled Flight Into Terrain.

3. System Component Failure – Powerplant.

4. Fuel Related.

5. Unknown or Undetermined.

6. System Component Failure – Non-Powerplant.

7. Unintended Flight In IMC.

8. Midair Collisions.

9. Low-Altitude Operations.

10. Other.