Philosophy includes the study of mathematical reasoning, but you don't get practice at it while you're studying it. It's like taking a music theory class versus learning to play an instrument.
Hm. When I was studying philosophy, we did have logic classes, and did diagram out the logic of arguments. It was a critical component for success in later courses, so I'd say we absolutely practiced it.
I own a modal logic textbook used by a course in a philosophy department, and on any given page it looks an awful lot like a math textbook except that the presentation is far friendlier and the explanations are better than are in 99% of math books.