Matthew modestly describes his calling in a few words:
He was busy at his job of collecting taxes: it was an activity detested by the Jews, because of suspicion of dishonesty, oppression and the main beneficiaries being the Romans of whom the Jews were vassals.
The Lord saw him and called him: no doubt, it would have been a tremendous surprise for Matthew, to be noticed by the great Master among so many people more popular than he, and on top of that being invited to be part of His group of disciples.
Matthew readily left everything to follow him: it is unlikely that Matthew did not already know about this great Rabbi, maybe he had even heard Him teaching. However, the Lord knew him perfectly, and chose him. Neither of them imposed conditions on the other to begin this so unique relationship. Matthew left an infamous work to become a disciple of the Lord, and became famous in the whole world until today, for being the author of one of the Gospels.
Luke tells us that Matthew, named Levi in Hebrew, gave the Lord Jesus a great feast, where there were many tax collectors (his colleagues at work, no doubt) and others who were with him at the table (Luke 5:27 -29). This must have been the same occasion. Matthew simply says Jesus and His disciples were having a meal in the house, when what he calls the "tax collectors and sinners" came and sat down with them. It was a contrast to the holiness of the Lord Jesus.
The Pharisees, who judged themselves superior because they ostensibly obeyed the Law of Moses, inquired of the Lord's disciples present, why did their Teacher eat with tax collectors and sinners. (They would certainly never descend to that level). The attitude of the Pharisees is still assumed by religious people nowadays, even believers, who do not want to be infected by the "wrong crowd". However, the sinners are in need of the Gospel, and a meal can be a good opportunity to give our testimony. We have to approach them.
The Lord Jesus gave them the answer: just as patients are those who need a doctor, are also sinners in need of repentance. The most serious disease, which affects humankind, is sin, and He came to bring healing. He cited Hosea 6:6: " I want mercy and not sacrifice" telling them that was what they should learn to practice.
God had established the sacrifices in the rituals of the Law of Moses, and the Pharisees were zealous in its fulfillment. However, the sacrifices did not replace the main commandment, which was to love God above all and your neighbour as yourself. The Pharisees were hard of heart, imposed upon the people heavy loads that they themselves did not carry and had no compassion for those who needed spiritual help.
Self-sacrifice without love of neighbour is worth nothing (1 Corinthians 13:3). The Pharisees were great sinners, as we are all (Romans 3:23). Maybe they were even greater sinners than those that were at the table with the Lord, because they did not admit their sin and did not seek to hear and obey the only Person who could give them salvation. They only gathered with others like themselves.
In contrast to them, the Lord Jesus said to them "I did not come to call the righteous, but sinners, to repentance" verse 13). He showed compassion for sinners, at the same time that he offered Himself as a sacrifice for them. As there are no righteous men in the world, He offered Himself for the entire world, and calls everyone to repentance. However, his calling only becomes effective when the sinner repents, thus acknowledging his sin. There is no cure for those who already consider themselves righteous, as the Pharisees.
John the Baptist, whose ministry was intended to prepare the people for the arrival of the Messiah, had disciples who had still stayed with him during the beginning of the ministry of the Lord Jesus.
They watched the disciples of Messiah, some of which had also been of John, and came to ask why they did not fast, as the disciples of John and the Pharisees did. It was criticism, because the ritual of fasting represented a lot to them.
To understand better what happened on that occasion, we must remember that John the Baptist still was a prophet of the Old Testament, and he and his disciples were still tied to the Law of Moses, with its precepts and rituals. He had presented the Messiah, and it was He that opened a new era, or dispensation, introducing the New Testament between God and humanity with the propitiation made with His blood.
The short ministry of the Messiah on earth was an interval during which He announced the beginning of His Kingdom and prepared His disciples for the new dispensation.
The "friends of the bridegroom" mentioned in the answer are an idiom of the time meaning the guests to a wedding. Fasting among the Jews was an act of self-denial due to sorrow and contrition. As the guests cannot show sadness in the presence of a groom at his wedding, it was not suitable for the disciples to demonstrate sadness while their Saviour was with them. However, there would be occasion for fasting when He returned to heaven, having completed the work of redemption that He had come to do, when He would be physically absent from His disciples.
There is no commandment to fast as there was in the Old Testament. Fasting is found together with prayer in the early church, on occasions when the direction of God was requested for making big decisions. In addition, in older versions it appears with prayer in 1 Corinthians 7:5. It is an act of self-denial in the face of God, approved here by the Lord Jesus.
Then the Lord uses two illustrations to show the change of dispensation from the Old Testament to the New Testament, and to teach that their principles should not be mixed:
The patch of new (unshrunk) cloth on an old garment, is like mixing the "law" and "grace": when the old garment is washed, the new patch will shrink, and rip the garment that has already gone through the process of shrinkage. It is going to be even more useless than before. At the beginning of the church, there were groups of judaizers in the church, who wanted to keep Judaism along with the Gospel of Christ. They were severely reprimanded by the apostle Paul in the Epistle to the Galatians, because it is not possible to maintain the freedom of the Gospel tied to precepts of the Law of Moses. Later came the clericalism (doctrine of the Nicolaitans), which developed into a priesthood and rituals that remind us of the Law of Moses, resulting in apostasy and idolatry, which had been the causes of rejection of Israel by God.
Putting new wine in old wineskins causes disruption of the wineskins because of fermentation of new wine (or grape juice). The old wineskins have less elasticity. The life and liberty of the Gospel ruin the precepts and rituals of the Law of Moses.
The usefulness of the Old Testament, with the Law of Moses, was at its end, and the Lord Jesus did not come to give it continuity through some patches because these could only worsen their situation. The Old Testament could not contain the Gospel of salvation only through faith in the redemptive work of Christ.
The Lord Jesus came to introduce a completely new garment, a completely new wine, to replace at once what existed at that time. The Apostle John shortens it like this, "the law was given through Moses; grace and truth came through Jesus Christ" (John 1:17).
9 As Jesus passed on from there, He saw a man named Matthew sitting at the tax office. And He said to him, "Follow Me." So he arose and followed Him.
10 Now it happened, as Jesus sat at the table in the house, that behold, many tax collectors and sinners came and sat down with Him and His disciples.
11 And when the Pharisees saw it, they said to His disciples, "Why does your Teacher eat with tax collectors and sinners?"
12 When Jesus heard that, He said to them, "Those who are well have no need of a physician, but those who are sick.
13 But go and learn what this means: 'I DESIRE MERCY AND NOT SACRIFICE.' For I did not come to call the righteous, but sinners, to repentance."
14 Then the disciples of John came to Him, saying, "Why do we and the Pharisees fast often, but Your disciples do not fast?"
15 And Jesus said to them, "Can the friends of the bridegroom mourn as long as the bridegroom is with them? But the days will come when the bridegroom will be taken away from them, and then they will fast.
16 No one puts a piece of unshrunk cloth on an old garment; for the patch pulls away from the garment, and the tear is made worse.
17 Nor do they put new wine into old wineskins, or else the wineskins break, the wine is spilled, and the wineskins are ruined. But they put new wine into new wineskins, and both are preserved."
Gospel of Matthew, chapter 9 verses 9 to 17