First, the defining thing, I forgot which episode it was but Red John killed Jane's childhood friend. How could someone find Jane's happiest memory and kill it? This person must have been with Jane in his childhood. Who could it be? His father.

Second, motivation. Jane was considered a traitor to his father when escaping with his wife. 

Third, Red John doesn't want Jane to die. Besides the fun of the catch game, reasons could be a) Jane could be of use, but it seems like Red John is always beyond Jane, why need him? b) Red John loves Jane. So, his father.

but something can't be explained: Red John also killed Jane's kid, that would be his grandchild if Jane's father is Red John. Is he so cold-blooded? maybe, since he abused Jane in the past.