A very tempting weakness
to create for oneself is that of moving the bishop's pawn. This happens
when the king's pawn (on e5) needs support. This can be very dangerous
for Black, however, when White still has his king's bishop. Opening up
the king this way lets the bishop take away one of the only two squares
for the king.
Greco's mate is very much like the back-row
mate. When Black creates an opening for the White rook, his own pawns
get in the way.
Notice that when the knight moves to e7,
it is double check. Once from the bishop and once from the knight. If
the knight moved to f4 instead, Black could interpose his rook
with Rf7. Since White would not be able to give check next move
without trading off his bishop, Black could give himself some freedom
by slipping in the move, g6.