It wasn't just heavy fog, it was also dark. Even if he was instrument rated, taking off in those conditions in a single engine aircraft is a really bad idea as you can't even land at your departure point if a mechanical issue develops.
In his case however he was not instrument rated, which puts this into serious Darwin award territory.
Sad report to read......you just have to wonder what he was thinking.
This is very unfortunate and it was absolutely unnecessary.
I'm sure the CFIs, Examiners, and the previous owner of the plane are all very sad today and second guessing their decisions to get this pilot in the air.
Glen Geller
1955 PA22-150 "One For Papa!"