10:38 NOTE: ...take his cross... Here is Jesus’ first mention of the word “cross” to His disciples (see note on 16:21).
"From that time Jesus began to show His disciples that He must go to Jerusalem, and suffer many things from the elders and chief priests and scribes, and be killed, and be raised up on the third day." Matthew 16:21
16:21 NOTE: ...From that time... This marks the beginning of a new emphasis in Matthew’s account. He turns his attention from Jesus’ public ministry, to His private instructions for the disciples, which took on a new, somber tone. The disciples had confessed their faith in Him as Messiah. From then on, He began to prepare them for His death.
10:38: Note Continued: ...take his cross... To them it would have evoked a picture of a violent, degrading death (see note on 27:31)
"After they had mocked Him, they took the scarlet robe off Him and put His own garments back on Him, and led Him away to crucify Him." Matthew 27:31
27:31 Note: ...to be crucified... Crucifixion was a form of punishment that had been passed down to the Romans from the Persians, Phoenicians, and Carthaginians. Roman crucifixion was a lingering doom—by design. Roman executioners had perfected the art of slow torture while keeping the victim alive. Some victims even lingered until they were eaten alive by birds of prey or wild beasts. Most hung on the cross for days before dying of exhaustion, dehydration, traumatic fever, or—most likely—suffocation. When the legs would no longer support the weight of the body, the diaphragm was constricted in a way that made breathing impossible. That is why breaking the legs would hasten death (John 19:31–33),
"Then the Jews, because it was the day of preparation, so that the bodies would not remain on the cross on the Sabbath (for that Sabbath was a high day), asked Pilate that their legs might be broken, and that they might be taken away. So the soldiers came, and broke the legs of the first man and of the other who was crucified with Him; but coming to Jesus, when they saw that He was already dead, they did not break His legs." John 19:31–33 (NAS)
27:31 Note Continued: but this was unnecessary in Jesus’ case. The hands were usually nailed through the wrists, and the feet through the instep or the Achilles tendon (sometimes using one nail for both feet). None of these wounds would be fatal, but their pain would become unbearable as the hours dragged on. The most notable feature of crucifixion was the stigma of disgrace that was attached to it,
"Christ redeemed us from the curse of the Law, having become a curse for us—for it is written, “Cursed is everyone who hangs on a tree” Galatians 3:13 (NAS)
"But I, brethren, if I still preach circumcision, why am I still persecuted? Then the stumbling block of the cross has been abolished." Galatians 5:11 (NAS)
"fixing our eyes on Jesus, the author and perfecter of faith, who for the joy set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God." Hebrews 12:2 (NAS)
27:31 Note Continued: One indignity was the humiliation of carrying one’s own cross, which might weigh as much as 200 pounds. Normally a quaternion, 4 soldiers, would escort the prisoner through the crowds to the place of crucifixion. A placard bearing the indictment would be hung around the person’s neck.
He was demanding total commitment from them—even unto physical death—and making this call to full surrender a part of the message they were to proclaim to others. This same call to life-or-death devotion to Christ is repeated in Matthew 16:24, Mark 8:34, Luke 9:23; 14:27. For those who come to Christ with self-renouncing faith, there will be true and eternal life (v. 39).
MacArthur, J. J. (1997). The MacArthur Study Bible (electronic ed.) (Mt 10:38). Nashville: Word Pub.