"You are Simon son of John. You will be called Cephas" (John 1:42)

Here Jesus is taking Peter as his disciple - naming him Cephas, meaning "like a stone."

Why is this? Because just as John the Baptist took on Jesus as his disciple, Jesus took on Peter as his disciple. And just as John took on other students and disciples, Jesus also followed in his footsteps and took on other students and disciples. This is a long-honored tradition among saintly teachers, and the basis for passing on the teachings of love for God.

Confirming this, we find practically every saint and prophet became a student under a saintly teacher. In some cases, the teacher was the father of the student. In other cases, a priest anointed the student:
"[God speaking]Anoint them just as you anointed their father, so they may serve Me as priests. Their anointing will be to a priesthood that will continue throughout their generations.” (Exodus 40:15)
This lineage of priests and their students becoming priests has continued through the centuries. In the case of David and Solomon we also know that David requested the priest Zadok and Nathan the prophet to take Solomon to Gihon. What happened in Gihon? The Old Testament says:
So Zadok the priest, Nathan the prophet, Benaiah son of Jehoiada, the Kerethites and the Pelethites went down and put Solomon on King David's mule and escorted him to Gihon. Zadok the priest took the horn of oil from the sacred tent and anointed Solomon. (1 Kings 38-39)
The presumption was that the "anointing" was merely the appointment of Solomon as king. Why would a priest have to do this, however? Why couldn't David simply just select Solomon and be done with it?

We also see this same "anointing" is considered in the book of Samuel, as it applies to Samuel and David:
Samuel did what the LORD said. When he arrived at Bethlehem, the elders of the town trembled when they met him. They asked, "Do you come in peace?"
Samuel replied, "Yes, in peace; I have come to sacrifice to the LORD. Consecrate yourselves and come to the sacrifice with me." Then he consecrated Jesse and his sons and invited them to the sacrifice.
When they arrived, Samuel saw Eliab and thought, "Surely the LORD's anointed stands here before the LORD."
But the LORD said to Samuel, "Do not consider his appearance or his height, for I have rejected him. The LORD does not look at the things man looks at. Man looks at the outward appearance, but the LORD looks at the heart."
Then Jesse called Abinadab and had him pass in front of Samuel. But Samuel said, "The LORD has not chosen this one either." Jesse then had Shammah pass by, but Samuel said, "Nor has the LORD chosen this one." Jesse had seven of his sons pass before Samuel, but Samuel said to him, "The LORD has not chosen these." So he asked Jesse, "Are these all the sons you have?"
"There is still the youngest," Jesse answered, "but he is tending the sheep."
Samuel said, "Send for him; we will not sit down until he arrives."
So he sent and had him brought in. He was ruddy, with a fine appearance and handsome features.
Then the LORD said, "Rise and anoint him; he is the one."
So Samuel took the horn of oil and anointed him in the presence of his brothers, and from that day on the Spirit of the LORD came upon David in power. Samuel then went to Ramah.(1 Samuel 16:1-13)
So we can see from this discussion that "anointing" was not simply the choosing of a king. The anointing process was taking place between one of God's loving servants (in this case, Samuel, who did the will of God) and someone that God has chosen to be anointed. Notice that after the anointing, "the Spirit of the Lord came upon David."

In other words, the "anointing" process was not the choosing of a king, but a ceremony that represented God's selection of one of His representatives. Note also that David was Jesse's son. Who was Samuel? David's spiritual teacher.

We can see the same tradition of teacher to student with respect to Samuel in the Old Testament:
The boy Samuel ministered before the LORD under Eli. In those days the word of the LORD was rare; there were not many visions. One night Eli, whose eyes were becoming so weak that he could barely see, was lying down in his usual place. The lamp of God had not yet gone out, and Samuel was lying down in the temple of the LORD, where the ark of God was. Then the LORD called Samuel. Samuel answered, "Here I am." And he ran to Eli and said, "Here I am; you called me." But Eli said, "I did not call; go back and lie down." So he went and lay down. Again the LORD called, "Samuel!" And Samuel got up and went to Eli and said, "Here I am; you called me."
"My son," Eli said, "I did not call; go back and lie down." Now Samuel did not yet know the LORD : The word of the LORD had not yet been revealed to him. The LORD called Samuel a third time, and Samuel got up and went to Eli and said, "Here I am; you called me."
Then Eli realized that the LORD was calling the boy. So Eli told Samuel, "Go and lie down, and if he calls you, say, 'Speak, LORD, for your servant is listening.' " So Samuel went and lay down in his place. The LORD came and stood there, calling as at the other times, "Samuel! Samuel!" Then Samuel said, "Speak, for your servant is listening."(1 Samuel 3:1-10)
So again we see here that Samuel had a spiritual guide and teacher, Eli, and "he ministered before the LORD under Eli". This illustrates the process of learning under a teacher and servant of God, as the path towards establishing our own relationship with God.

Notice also how Eli called Samuel "son" even though Samuel was not actually his genetic offspring. Samuel was Eli's student.

This tradition continued throughout the Old Testament, even to Jesus' day. When John the Baptist hesitated to baptize ("anoint") Jesus, Jesus said:
“Let it be so now; it is proper for us to do this to fulfill all righteousness.” (Matt 3:15)
Remember that Jesus also took on disciples.

This indicates a continuation of the process of handing down God's message from teacher to student. It is the process that God has empowered, because God enables us to come to know Him through His loving servants. This process concludes in the student also following in the footsteps of his teacher, and working to pass on God's message just as his teacher did.

This is the process that is empowered by the Supreme Being.

(The New International Version was used in the above Biblical quotes. Also consider the Gospels of Jesus for Jesus' statement above - from the original Greek texts without ecclesiastical sectarian influence.)