I like your thinking but you cannot put your own king in check. Think of it this way-- if instead of checkmate, you had to capture the opponents king to win the game, and white was to move and captured the bishop, black would take the king with the pawn the next move to win the game. Good luck with your chess!
Why wouldn't the game let me move KF5?
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Why wouldn't the game let me move KF5 to capture bishop? The pawn on E6 is pinned by the rook right?