The opening passages of Luke lay out a number of important themes. But few events are as staggering as the rejection of Jesus in his hometown. The other three gospels record these events without mentioning the actually teaching of Christ that spurred the event (Matthew 13:53-58; Mark 6:1-6; John 4:44). Christ is in his hometown teaching in the synagogue and the lectionary text of Isaiah,

The Spirit of the Lord God is upon me,
Because the Lord has anointed me
To bring good news to the afflicted;
He has sent me to bind up the brokenhearted,
To proclaim liberty to captives
And freedom to prisoners; - Isaiah 61:1

The response of the people was one of doubt and confusion. It was the lineage of Jesus through Joseph that confused the people. Yet, this is the very lineage that Luke's gospel discredits when it states "as was supposed, the son of Joseph" (Luke 3:23). On this Erasmus said, "For the people, being offended at the lowliness of his person, cannot help but doubt the doctrine and the offices of Christ" (Reformation Commentary on Scripture: Luke,  102). Simplified, the people were disturbed at Christ's lowly form and were already wanting — in their thoughts and hearts — external signs to be performed. 

Both of these concepts help to explain why Christ's responds with an accusation and a promise to go to the lowly with mighty signs. First, Christ predicts his death on the cross and the betrayal of Israel before quoting the repeated phrase that "no prophet is welcome in his hometown" (Luke 4:23-24). This is the accusation against what is in their hearts. Second, and unlike the other gospels, Luke ties the lowliness of Jesus to his ministry, filling out the full meaning of this event. For here Christ at the beginning of his ministry makes a pronouncement that certainly altered the perception of his Jewish audience — the real miracles will occur among the Gentiles. 

"There were many widows in Israel in the days of Elijah, when the sky was shut up for three years and six months, when a great famine came over all the land; and yet Elijah was sent to none of them, but only to Zarephath, in the land of Sidon...And there were many lepers in Israel in the time of Elisha the prophet; and none of them was cleansed, but only Naaman the Syrian." - Luke 4:25-27

It is in response to these words from Jesus — still having just sat down in the synagogue after reading — that causes the crowd to rage. Not only has Jesus proclaimed himself the fulfillment of Isaiah, but now he is indicating that the true fulfillment of "good news to the afflicted" and "bind up the brokenhearted" might not be to the people of Israel. That ultimately that "freedom to prisoners" expected in the Jewish Messiah would be first given to the world and the nations (Romans 9-11).

The crowd in their rage drove Jesus out to the crest of the hill (the word usually translate for mountain) in a plot to kill Him. And yet, upon reaching the hill Christ walks out of their midst. There is some symbolism here that may or may not be intentional. In Israel's past, God met with them on mountains and here Christ departs from them leaving them alone on the mountain. The symbolism in the context of the passage may be intentional. With reference to magnitude, God is going to pass over Israel in the glory and miraculous nature of the gospel. Seeing different symbolism, Cyril of Alexandria wrote, "So they threw him out of their city, pronouncing by their action their own condemnation...They themselves were banished from the city that is above, for not having received Christ" (Ancient Christian Commentary: Luke, 82).

Both symbols would speak not only to this situation but also the larger rejection of Christ by the people of Israel. Paul would later say that Isaiah was referring to these rejections even during his day,

What shall we say then? That Gentiles, who did not pursue righteousness, attained righteousness, even the righteousness which is by faith; but Israel, pursuing a law of righteousness, did not arrive at that law. Why? Because they did not pursue it by faith, but as though it were by works. They stumbled over the stumbling stone - Romans 9:30-32

But I say, surely Israel did not know, did they? First Moses says,

“I will make you jealous by that which is not a nation,
By a nation without understanding will I anger you.”
And Isaiah is very bold and says,

“I was found by those who did not seek Me,
I became manifest to those who did not ask for Me.”
But as for Israel He says, “All the day long I have stretched out My hands to a disobedient and obstinate people.” - Romans 10:19-21

Luke's gospel is influenced by Paul's theology. And it intentionally colors the events of Christ's ministry with the Jewish rejection of Christ (and Paul in Acts). Placed at the front of his gospel, Luke actively sets the precedent — the Gentiles shall be blessed.