What's the difference between
reason for x
reason why x
reason that
Some examples are:
The police asked her the reason for her visit.
The reason why so many people caught the disease is still not clear
The reason these cars are so expensive is that they are largely built by hand
All three phrases can be used interchangeably depending on context.
In your usage
reason for
is used to focus on motivation or existance
The police asked her the reason for her visit.
The police asked her the reason why she visited.
The police asked her for the reason that she visited (here).
reason why
is used to focus on causality
The reason why so many people caught the disease is still not clear.
The reason for so many people catching the disease is still not clear.
The reason that so many people caught the disease is still not clear.
reason that
is used to explain why something happened or exists
The reason that these cars are so expensive is because they are largely built by hand.
The reason why these cars are so expensive is because they are largely built by hand.
The reason for these cars being so expensive is because they are largely built by hand.
In each group of examples, the three sentences have the same meaning, the usage is basically stylistic.
