"Woe to you, teachers of the law and Pharisees, you hypocrites! You build tombs for the prophets and decorate the graves of the righteous. And you say, 'If we had lived in the days of our ancestors, we would not have taken part with them in shedding the blood of the prophets.' So you testify against yourselves that you are the descendants of those who murdered the prophets. Go ahead, then, and complete what your ancestors started!" Matt. 32:29-31 (NIV)
"Nevertheless, I must go on my way today and tomorrow and the day following, for it cannot be that a prophet should die outside of Jerusalem." Luke 13:33
Why did Jesus die? Jesus said explicitly why he was going to allow himself to be killed: "This is My commandment, that you love one another as I have loved you. Greater love has no one than this, than to lay down one’s life for his friends. You are My friends if you do whatever I command you." (John 15:12-14)
So, Jesus died because laying down his life was the greatest form of love. For whom? His friends. Who are his friends? Those who obey his word, which will never become irrelevant (Mark 13:31.) Jesus' death was the ultimate fulfillment of his ministry of love, compassion and self-sacrifice.
Therefore, when Jesus says "It is finished" on the cross (John 19:30) it cannot possibly mean that our requirement to do Good Works is finished, or that our need to go to God to seek forgiveness is finished, or that our duties to serve others is finished. It cannot ever mean any of those things, or Jesus' ministry was in vain.
Let us remain always his friends by seeking to always follow his teachings. Let us not make his death be in vain!