WHen YOU lose and it says finish him for the OPPONENT, you type in the buttons. Hara kiris are meant to be done before your opponent can do his/her fatality. You lose the match either way cuz say yur Darrius and you're fighting sub zero, if you lose and do your hara kiri when it says finish him it'll say "Sub Zero Wins...Hara-Kiri!" So while there's not necessarily a point to hara kiris, its mainly to steal your opponents chance of giving you a fatality cuz you take yourself out. So in short, you press the buttons when you LOSE the match and it says finish him.
