Day 79 / 286 to go

Today I worked with Edourd`s "Avoidable Mistakes" - again trying to solve puzzles (but all being based on real games - not like Lommer). Here is a one I didn´t get (Black to move):

Actually, even after consulting the solution, I still don´t get it:  I went for Bf4. Although Kf8 crossed my mind for a minute, I couldn´t see why it would be better than Bf4...  Best move is - according to the book - Kf8, but why?  Any hint?