Imagine a prisoner on death row. The governor's son, who is innocent, voluntarily takes the prisoner's place in the electric chair and dies for him. The prisoner is pardoned and set free (this is Jesus dying for us).

Now, the freed prisoner is invited to come live and work in the governor's mansion. However, he still has the habits, language, and loyalties of a criminal. To live well in the new life, he must "die" to his old identity, his old gang, and his old ways. This daily choice to leave the old life behind is what it means to die with Christ. He doesn't do this to earn his freedom—that was already granted. He does it because he has been given a new life and a new identity.

Christianity is not the disciples dying for Jesus but Jesus dying for His disciples establishing the sole basis of our salvation.

However, it is incomplete without the biblical truth that those who are saved by Jesus's death for them are then called to participate in His death with him. This "dying with" is the necessary and joyful response of a life transformed by grace. It is the way we live out the reality of what He has accomplished for us.

In summary: He died for us to save us from the penalty of sin. We die with Him to be saved from the power of sin in our daily lives. Both are explicitly biblical and essential to the faith.

Matthew 9:17

17 Neither do men put new wine into old bottles: else the bottles break, and the wine runneth out, and the bottles perish: but they put new wine into new bottles, and both are preserved.