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If anyone wishes to come after Me, let him deny himself, and take up his cross, and follow Me (Mark 8:34).
Again, note that Jesus' words were addressed to anyone who wished to come after Him, anyone who wanted to become His follower. This is the only relationship Jesus initially offers—to be His follower.
Many desire to be His friend without being His follower, but such an option does not exist. Jesus didn't consider anyone His friends unless they obeyed Him. He once said, "You are My friends, if you do what I command you" (John 15:14).
Many would like to be His brother without being His follower, but, again, Jesus didn't extend that option. He considered no one His brother unless he was obedient: "Whoever does the will of My Father who is in heaven, he is My brother" (Matt. 12:50, emphasis added).
Many wish to join Jesus in heaven without being His follower, but Jesus conveyed the impossibility of such a thing. Only those who obey are heaven-bound: "Not everyone who says to Me, 'Lord, Lord,' will enter the kingdom of heaven; but he who does the will of My Father who is in heaven" (Matt. 7:21).
In the sentence under consideration, Jesus informed those who wanted to follow Him that they couldn't follow Him unless they denied themselves. They must be willing to put their desires aside, making them subordinate to His will. Self-denial and submission is the essence of following Jesus. That is what it means to "take up your cross."