They were tempting Jesus not to die on the cross but to live.

When Jesus was on the cross, people passing by shook their heads and mocked Him, saying, "You who are going to destroy the temple and rebuild it in three days, if you are the Son of God, save yourself and come down from the cross."  The chief priests, along with the teachers of the law and the elders, also mocked Him, saying, "He saved others, but He cannot save Himself.  He is the King of Israel!  Let Him come down now from the cross, and we will believe in Him.  He trusts in God; let God rescue Him now if He wants Him, for He said, 'I am the Son of God.'"  Even the robbers who were crucified with Him heaped insults on Him (Matthew 27:38-44, Modern Korean Bible). 

When I meditated on these verses, I thought that just as Jesus was tempted by the devil before He began His public ministry (4:1-11), He was also tempted by the devil’s agents (1) "the people passing by," (2) "the chief priests," "the teachers of the law and the elders," and (3) the two "robbers" crucified with Him while He was on the cross.  In short, the temptation can be summarized as: "Save yourself from the cross." In other words, they were tempting Jesus not to die on the cross but to live.

When we face such temptations, if we, like the apostle Peter, fall into Satan’s temptation and think only of human matters rather than God’s work, we may refuse to take up our cross and seek to save our lives.  However, if we are filled with the Holy Spirit and think of God’s work, we will obey Jesus’ words, take up our cross, follow Him, and lay down our lives for Him. Jesus’ words are: "Whoever wants to save their life will lose it, but whoever loses their life for me will find it" (Ref.: 16:22-25, Modern Korean Bible).