Matthew 10:38 is the first reference to the cross in Matthew. This does not refer to the Cross of Christ, but to the Roman custom of crucifixion. They had crucified literally hundreds of thousands of people. The Jews understood what it meant to take up the cross. Rome had crucified many of the Jews for different offenses.
“And he who does not take his cross and follow after Me is not worthy of Me.” (Matthew 10:38, NASB)
It was the Roman custom for the condemned person to carry his own cross to the point of execution. It was a sign of both condemnation and disgrace to be seen carrying a cross. In this context, carrying the cross represents giving up the greatest things in life to put Bible doctrine ahead of all else. For example, going overseas in missionary work when you are very close to your in-laws or very effective in teaching the Word in your home country. This is putting doctrine before anyone or anything else.
The Lord was not thinking of His own crucifixion. However, this is a perfect illustration. In going to the Cross to die for our sins, Jesus had to sever his own family connections. In the first three hours, He severed His human family connections. He fulfilled another of the many statutes of the Mosaic Law in John 19:27 by asking John the disciple to care for His mother after He was gone. In effect, John was given the responsibility of caring for Mary as a family member for as long as she would live.
“Then He said to the disciple, “Behold, your mother!” From that hour the disciple took her into his own household.” (John 19:27, NASB)
In the last three hours when His humanity was bearing our sins, the family connections with God the Father were severed. God could not look upon sin when His Son was bearing it. Only the omnipotence of Holy Spirit could sustain His humanity during that judgement for our sins. Psalms 22:1.
“For the choir director; upon Aijeleth Hashshahar. A Psalm of David. My God, my God, why have You forsaken me? Far from my deliverance are the words of my groaning.” (Psalms 22:1, NASB)
When He had finished bearing our sins, He again was restored to fellowship and voluntarily dismissed His human spirit and died physically. Luke 23:46.
“And Jesus, crying out with a loud voice, said, “Father, INTO YOUR HANDS I COMMIT MY SPIRIT.” Having said this, He breathed His last.” (Luke 23:46, NASB)