First, the cross is offensive because of the type of people that were crucified on a cross. The worst of the worst of criminals in Roman society. The fact that the God of the universe would have anything to do with such a type of penalty was an offense. The image of a crucified man represented weakness, shame, and disgrace. Christ being crucified was both a stumbling block to the Jews and folly to the Gentiles (1 Cor. 1:23).
Second, the cross is offensive because it exposes our own spiritual condition. The cross is humiliating to us as man because it shows that there is absolutely nothing that we can do in order to earn Gods' favor. It says that even our good works are like filthy rags (Isa. 64:6); which also reveals that the human nature is not good but rather sinful. This make the cross, the gospel, offensive because in our best efforts we will always fail and are lost. It took the death of Jesus on the cross in order to have any means of justification before God. So we are helpless and lost in our own sin without the cross.
Third, the cross is offensive because it is exclusive in its message. The cross claims that the only way of justification before God is through the death of Jesus on the cross. There is no other form of forgiveness given so stop trying to display your own righteousness (filthy rags). It is offensive to mankind to claim that Jesus is the only way of salvation and the only way to have a restored relationship with God.
The cross is offensive for many more reasons than the three brief reasons we examined above. Without the cross we lose a significant part of the salvation message we proclaim. The offense as Paul stated in Galatians 5:11 is one that is meant to last forever; because the message of the cross is offensive to all men everywhere throughout history. And until Christ himself returns and all eyes are fully opened, it will only continue to be offensive to those that are perishing.
How are you displaying the cross in your own life? Are you living in such a way that your life demands an explanation?