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Matthew 27:42
42"He saved others; he cannot save himself. He is the King of Israel; let him come down now from the cross, and we will believe in him."
The religious leadership gathered around the cross in an attempt to drive home their conviction that Jesus was not the Messiah (king of Israel), and especially not the Son of God. I imagine many in the crowd felt animosity toward Rome for carrying out the execution, but some were probably disillusioned with their own leaders. That is why those leaders thought it necessary to make a public display of what they thought was Jesus' helplessness. We see their envy displayed in all its ugliness as they mocked the One whom they perceived was their competition for the respect of the people.
Jesus was tempted in the wilderness to prove He was the Son of God by throwing Himself off a high point in front of the crowds (Matthew 4:5-7). This is the same kind of temptation set before Him with words of this nature: "If you miraculously come down from the cross, we will believe you are the Son of God, the Messiah." But would they really? When He did something even more impossible, rising from death, they did not believe.
I have heard people say they will believe if they see a vision of Jesus telling them He is the only way to God. It does happen, especially in nations closed to the gospel. But in most cases, people who say they need a sign are like these religious leaders. It is an excuse to not believe and go about their selfish lives. God is pleased with faith. God has given us signs in nature and the Scriptures. He will even give us more, if we truly would believe. But He will not give us greater signs if they will only be a witness against us on the Day of Judgment.
Consider: The leaders acknowledged that Jesus saved others. He could have come down from the cross. However, He chose not to save His own physical life in order that He might save every soul that would come to Him. There are none as blind as those who choose not to see.