If White withdraws his light-squared bishop along the b1-h7 diagonal, then Black is facing two mate threats: White can move his king off the a-file, discovering mate by the a8 rook, or he can move his dark-squared bishop off the first rank, discovering mate by the h1 queen. A few sample lines:

1. Bf5 Rxa8+ 2. Ba7#
1. Bf5 Rxh1 2. Kb3#
1. Bf5 Rh4 [ready to block a rook check or take the queen] 2. Bh2#
1. Bf5 Rd8 [ready to block a queen check or take the rook] Bd4#
(If 1. Bf5 c2 then 1. Bd4#!)

At first it looks as though Black is doomed, but he does have one resource. If after e.g. 1. Bf5 he plays 1. … Rg8 then White has no way to mate on the next move: If the white king discovers check, Black can simply take the rook, and if the g1 bishop discovers check by the queen, the rook can interpose.

The answer is 1. Bg6!, the only initial bishop move that blocks the rook’s route to g1 and keeps both mate threats alive.