Commentaries:
Why does Christ have to say things like this? Because human nature is driven by the impulse that the only way to the things a person deeply desires is through self-centered, assertive, competitive concentration on getting what it wants. We all have this drive; however, individuals differ in the strength of human nature in them and the methods they employ to achieve their goals. Jesus says the self must be denied because human nature is driven by pride and covetousness.
Of course, the Bible is not urging us to court martyrdom. It is speaking of a general approach to life, of crucifying the self-centered impulses of human nature. This means subordinating a clamoring ego with its preoccupation with "I," "me," and "mine"; its concern for self-assertion; and its insistence on comfort and prestige. It is denying the self for the sake of embracing Christ's cause. To be ashamed to live this way of life is equivalent to being ashamed of Christ Himself.
John W. Ritenbaugh
The Elements of Motivation (Part Six): Eternal Life
Jesus teaches self-denial to His disciples not only with His words but also by His actions. Notice that His call to self-denial comes immediately after predicting His own sacrificial death. He is the supreme model of the self-denial to which He calls others. He even denies Himself any urge to avenge Himself or to threaten His persecutors for what they had done to Him. In Jesus' example, we see that, by committing ourselves to God who judges rightly, we deny ourselves the temptation of worldly lusts.
Martin G. Collins
Overcoming (Part 5): Self-Denial
Other Forerunner Commentary entries containing Mark 8:34:
Matthew 9:27-30
Luke 6:46
John 12:20-26