I'm working through Silman's "Complete Endgame Course" and I've bumped into an example I'm having some trouble with. I understand the theory of the following position which is basically: Black can not exchange bishops because white will win the K+2P vs. K endgame. White can not allow the black bishop any pawn captures that leaves white with only an h-file pawn as that is a drawn endgame. The problem I have is with Silman's example. I can't make much sense out of it and thought I'd ask you folks to take a look at it. Here is the position and the moves given in the example.

I think 1... Bg4 makes things more difficult for white. The white king will be forced to return to the pawns. I think the immediate 1. Bf5 is a stronger move for white than 1. Ke5. Am I missing something?

Seems to me you are right. But it does not matter either way. The result is the same.

From what I've figured out, black shouldn't leave the d1-h5 diagonal until absolutely forced to do so. Then black should do everything possible to take white's g pawn. In your example I think black is better off playing ...Be2 than ...Bf7. If white advances the g pawn black's bishop can just capture it with a drawn game. I've done a bit of practice with this position and I see that it's a forced win. It just doesn't seem remotely close to as easy as Silman's example makes it look. I thought I must be overlooking something but I can't find what it is.