I got asked if I make a difference between why and what for, and to be honest: It depends. In contexts of my work, when I want to open up a group of people for this kind of refreshing the perspective generally (i.e. that there is a certain meaning underneath every action and strategy f.e. of a parish or a organization), I use those questions in an equal or at least quite similar way.
At our last course someone mentioned that he got trained to avoid asking why, and I am aware of this risk: There are situations and contexts where repeatedly asking why is a strategy to boycott or protest in some way or another. In this situations is it better to ask what for, certainly. Because this brings up a productive emphasis on this perspective.
But if there is enough time, I try to set different accents: A why has to catch me in the first place, a what for is primarily eccentric or productive. This difference brings people of parishes and christian communities back to their own stories about calling, conversions and redemption, which for me is the first step of becoming and being church in an refounded way.
By the way: This is one of the cores of my dissertation project about the mission-shaped church (and fresh expressions of church) in the context of a roman-catholic ecclesiology.