Why can't I capture the king???

Consider this position. By the rules of chess, black is in check, but should he be? White would have to make an illegal move to capture the black king with the knight. An variant could have a rule that says "A king is in check if a piece could capture it by making a legal move."

Nahh black's bishop is too sad to eat white's king after the knight eats his king

Another chess variant could be that black gets to play the same number of moves as white. So in this position, if white captures the black king, black could capture the white king, and it would be a draw. It would need another rule that says kings are captured, not checkmated, and exposing your king to attack is legal.