One of the more popular ways to describe Jesus' death is substitution; He died in our place. While the writers of the Bible described Jesus' death as a substitution, that wasn't the only way they talked about it.
Jesus' death is an invitation to us to take up our own cross and follow Him.
And he who does not take his cross and follow after Me is not worthy of Me. He who has found his life will lose it, and he who has lost his life for My sake will find it.Matthew 10:38–39
Just as Jesus gave His life for us, He wants us to lay down our lives for others.
This is My commandment, that you love one another, just as I have loved you. Greater love has no one than this, that one lay down his life for his friends. You are My friends if you do what I command you.John 15:12–14
This is what Paul had in mind in Philippians 2 when he told the church to regard one another as more important than themselves.
Therefore if there is any encouragement in Christ, if there is any consolation of love, if there is any fellowship of the spirit, if any affection and compassion, make my joy complete by being of the same mind, maintaining the same love, united in spirit, intent on one purpose. Do nothing from selfishness or empty conceit, but with humility of mind regard one another as more important than yourselves; do not merely look out for your own personal interests, but also for the interests of others. Have this attitude in yourselves which was also in Christ Jesus…Philippians 2:1–5
We lay down our lives for others through being patient in disagreements, attempting to understand people's opinions, and by lifting each other up, even if we don't agree with someone's beliefs.
Now accept the one who is weak in faith, but not for the purpose of passing judgment on his opinions.Romans 14:1
In doing this, we imitate Christ by crucifying ourselves with Him and entrusting ourselves to the resurrecting power of God.
Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life.Romans 6:4
When we live a life of sacrifice, resurrection follows. We allow Jesus to live through us, which means dying for others when necessary and being lifted up by God always.
I have been crucified with Christ; and it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself up for me.Galatians 2:20
Humble yourselves in the presence of the Lord, and He will exalt you.James 4:10
While discussing Jesus' death as a substitution has its place, ultimately we must move from a non-participatory view of the Cross to one that requires us to die beside Jesus, allowing Jesus' death to work through us, saving those around us.