Overview
Family: Spiritual versus Earthly
The simplest idea here is that his spiritual family is more important than his earthly one, a central teaching of Jesus.
Compare:
Luke 8:19-21
Then his mother and his brothers came to him, but they could not reach him because of the crowd. And he was told, "Your mother and your brothers are standing outside, desiring to see you." But he answered them, "My mother and my brothers are those who hear the word of God and do it."
Luke 12:51-53
Do you think that I have come to give peace on earth? No, I tell you, but rather division. For from now on in one house there will be five divided, three against two and two against three. They will be divided, father against son and son against father, mother against daughter and daughter against mother, mother-in-law against her daughter-in-law and daughter-in-law against mother-in-law.
Luke 14:26
If anyone comes to me and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple.
Echoes: Joseph
The parallels to the account of Joseph are strong, with Joseph's early dreams upsetting his parents because they are displaced. Little did Jacob know just how much distress he would go through seeking his son, let alone the shock of actually finding him in such a situation as turned out to be the case.
Compare:
Genesis 37:9-11
Then he dreamed another dream and told it to his brothers and said, "Behold, I have dreamed another dream. Behold, the sun, the moon, and eleven stars were bowing down to me." But when he told it to his father and to his brothers, his father rebuked him and said to him, "What is this dream that you have dreamed? Shall I and your mother and your brothers indeed come to bow ourselves to the ground before you?" And his brothers were jealous of him, but his father kept the saying in mind.
Foreshadows: Death and Resurrection
This account also clearly prefigures his resurrection. At the time of the Passover, Jesus goes to Jerusalem, where he disappears for three days. When he is found, he has had no terrible fate befall him, but rather asks, "Why were you looking for me?"
Luke 22:1-2
Now the Feast of Unleavened Bread drew near, which is called the Passover. And the chief priests and the scribes were seeking how to put him to death, for they feared the people.
Luke 23:42-43
And he said, "Jesus, remember me when you come into your kingdom." And he said to him, "Truly, I say to you, today you will be with me in paradise."
Luke 24:2-7
And they found the stone rolled away from the tomb, but when they went in they did not find the body of the Lord Jesus. While they were perplexed about this, behold, two men stood by them in dazzling apparel. And as they were frightened and bowed their faces to the ground, the men said to them, "Why do you seek the living among the dead? He is not here, but has risen. Remember how he told you, while he was still in Galilee, that the Son of Man must be delivered into the hands of sinful men and be crucified and on the third day rise."
Luke 2:41-52
Luke 2:41
Now his parents went to Jerusalem every year at the Feast of the Passover.
every year
Joseph and Mary are godly, dedicated Jews.
Feast of the Passover
Luke 22:1
Now the Feast of Unleavened Bread drew near, which is called the Passover.
Luke 2:42
And when he was twelve years old, they went up according to custom.
Luke 2:43
And when the feast was ended, as they were returning, the boy Jesus stayed behind in Jerusalem. His parents did not know it,
boy
This word in Greek (παῖς) means "child" and is often used as a term for a servant. It carries a sense of endearment with it; the young man Eutychus in Acts 20:9 who fell from the third story is called by this term in 20:12, "And they took the youth away alive, and were not a little comforted."
Acts 3:13, 26
The God of Abraham, the God of Isaac, and the God of Jacob, the God of our fathers, glorified his servant (or child) Jesus, whom you delivered over and denied in the presence of Pilate, when he had decided to release him.
...God, having raised up his servant (or child), sent him to you first, to bless you by turning every one of you from your wickedness.
Luke 2:44
but supposing him to be in the group they went a day's journey, but then they began to search for him among their relatives and acquaintances,
Luke 2:45
and when they did not find him, they returned to Jerusalem, searching for him.
Luke 2:46
After three days they found him in the temple, sitting among the teachers, listening to them and asking them questions.
After three days
Luke 24:7
The Son of Man must be...crucified and on the third day rise.
Luke 2:47
And all who heard him were amazed at his understanding and his answers.
Luke 2:48
And when his parents saw him, they were astonished. And his mother said to him, "Son, why have you treated us so? Behold, your father and I have been searching for you in great distress."
Son
The Greek for "son" here (τέκνον) is the word for the one to whom you gave birth. This phrasing indicates mother wishes to assert some authority over her child.
why have you treated us so...? your father and I...in great distress....
There is an eerie inverse example of this verse in Luke 16:25, "But Abraham said, 'Child (or, son), remember that you in your lifetime received your good things, and Lazarus in like manner bad things; but now he is comforted here, and you are in anguish (or, distress)."
Luke 2:49
And he said to them, "Why were you looking for me? Did you not know that I must be in my Father's house?"
Why were you looking for me?
Luke 24:5
And as they were frightened and bowed their faces to the ground, the men said to them, "Why do you seek the living among the dead?"
in my Father's house
One wonders where the translators got "house" from. The Greek uses an implied, not specified term, literally rendered, "I must be in/among the [masculine plural things] of my Father."
A better rendering might be, "among the people of my Father," which follows the grammar well, contrasts with the original search for him among their relatives (verse 44), and fits the theme of this story contrasting his earthly family with his spiritual one.
Luke 2:50
And they did not understand the saying that he spoke to them.
they did not understand
It is a recurrent theme that Jesus said many things not understood when spoken but remembered later.
Luke 9:45
But they did not understand this saying, and it was concealed from them, so that they might not perceive it. And they were afraid to ask him about this saying.
John 12:16
His disciples did not understand these things at first, but when Jesus was glorified, then they remembered that these things had been written about him and had been done to him.
Acts 7:25
He supposed that his brothers would understand that God was giving them salvation by his hand, but they did not understand.
the saying that he spoke to them
This is not just an awkward translation that could have been better as "what he said." The translators are calling attention to the fact he is putting forth something for them (and us) to remember and to grapple with in our understanding.
See "Appendix: And they remembered his words"
Luke 2:51
And he went down with them and came to Nazareth and was submissive to them. And his mother treasured up all these things in her heart.
was submissive
The Greek here (ὑποτάσσω) means he obeyed them, or was their subordinate. Children must obey their parents in the teaching of the Lord.
Hebrews 12:9
We have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live?
Romans 13:1
Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God.
1 Peter 5:5
Likewise, you who are younger, be subject to the elders. Clothe yourselves, all of you, with humility toward one another, for "God opposes the proud but gives grace to the humble."
treasured up all these things in her heart
These "things" (ῥῆμα) are more than just this episode. It includes what he said to them which they did not understand (verse 50), but also several other things earlier in this gospel.
(See "Appendix: And they remembered his words".)
When taken together, these references tell us Mary was Luke's source for the events in this part of his gospel.
Genesis 37:11
And his brothers were jealous of him, but his father kept the saying in mind.
Luke 2:19
Mary treasured up all these things, pondering them in her heart.
Luke 2:52
And Jesus increased in wisdom and in stature and in favor with God and man.
favor with God and man
The same is ascribed to Mary earlier in this gospel, Luke 1:30, "And the angel said to her, 'Do not be afraid, Mary, for you have found favor with God.'"
Proverbs 3:1-4
My son, do not forget my teaching,
but let your heart keep my commandments,
for length of days and years of life
and peace they will add to you.
Let not steadfast love and faithfulness forsake you;
bind them around your neck;
write them on the tablet of your heart.
So you will find favor and good success
in the sight of God and man.