In many instances, Christ used the word "Generation" to call out the unbelieving people, Why Christ used the word "Generation"? who are those people?
What shall I compare this generation?
16.But to what shall I compare this generation? It is like children sitting in the marketplaces and calling to their playmates, 17.‘We played the flute for you, and you did not dance; we sang a dirge, and you did not mourn.’ 18.For John came neither eating nor drinking, and they say, ‘He has a demon.’ 19.The Son of Man came eating and drinking, and they say, ‘Look at him! A glutton and a drunkard, a friend of tax collectors and sinners!’ Yet wisdom is justified by her deeds - Matthew 11:16-19
This incident happened at the initial days of Christ's ministry, here, the people supposed to be excited for God came into this world, instead, they tried prove Jesus Christ as an ordinary man, in that circumstances, Christ called them as "this generation", basically the people those who want to continue their life as a children(generation) of their worldly identity like "i am a disciple of john", "i am a jew", "i am a pharisee", "i am from chorazin", "i am from bethsaida" etc. and do not want to become a children of God.
An evil and adulterous generation
38.Then some of the scribes and Pharisees answered, saying, “Teacher, we want to see a sign from You.” 39.But He answered and said to them, An evil and adulterous generation seeks after a sign, and no sign will be given to it except the sign of the prophet Jonah. 40.For as Jonah was three days and three nights in the belly of the great fish, so will the Son of Man be three days and three nights in the heart of the earth. 41.The men of Nineveh will rise up in the judgment with this generation and condemn it, because they repented at the preaching of Jonah; and indeed a greater than Jonah is here. 42.The queen of the South will rise up in the judgment with this generation and condemn it, for she came from the ends of the earth to hear the wisdom of Solomon; and indeed a greater than Solomon is here - Matthew 12:38-42
And in another incident, Christ called the scribes and pharisees as "an evil and adulterous generation", because even after Jesus Christ did so many miracles which can be done only by God, in fact, those miracles are mentioned in the old testament as an identity of the coming Messiah, the scribes and pharisees asked Jesus Christ to prove himself as Son of God, and those people are identified as "an evil and adulterous generation" by our Lord Jesus Christ, because they are happy with their worldly identity, and do not want to become a children of God.
Adulterous and sinful generation
For whoever is ashamed of Me and My words in this adulterous and sinful generation, of him the Son of Man also will be ashamed when He comes in the glory of His Father with the holy angels - Mark 8:38
And again, here some of them want to save their life by themself, and they don't want Jesus Christ in their life, and Christ called them as "adulterous and sinful generation".
It shall be required of this generation
42.But woe to you Pharisees! For you tithe mint and rue and all manner of herbs, and pass by justice and the love of God. These you ought to have done, without leaving the others undone. 43.Woe to you Pharisees! For you love the best seats in the synagogues and greetings in the marketplaces. 44.Woe to you, scribes and Pharisees, hypocrites! For you are like graves which are not seen, and the men who walk over them are not aware of them.” 45.Then one of the lawyers answered and said to Him, “Teacher, by saying these things You reproach us also.” 46.And He said, “Woe to you also, lawyers! For you load men with burdens hard to bear, and you yourselves do not touch the burdens with one of your fingers. 47.Woe to you! For you build the tombs of the prophets, and your fathers killed them. 48.In fact, you bear witness that you approve the deeds of your fathers; for they indeed killed them, and you build their tombs. 49.Therefore the wisdom of God also said, ‘I will send them prophets and apostles, and some of them they will kill and persecute,’ 50.that the blood of all the prophets which was shed from the foundation of the world may be required of this generation, 51.from the blood of Abel to the blood of Zechariah who perished between the altar and the temple. Yes, I say to you, it shall be required of this generation - Luke 11:42-51
Here some of them identified themselves as scribes, pharisees, and lawyers, and they are so proud about their family genealogy, always talking about their family proud, and do not care about the born again life, and Christ called them as "this generation" and said "Woe to you".
Rejected by this generation
24.For as the lightning that flashes out of one part under heaven shines to the other part under heaven, so also the Son of Man will be in His day. 25.But first He must suffer many things and be rejected by this generation. 26.And as it was in the days of Noah, so it will be also in the days of the Son of Man: 27.They ate, they drank, they married wives, they were given in marriage, until the day that Noah entered the ark, and the flood came and destroyed them all. 28.Likewise as it was also in the days of Lot: They ate, they drank, they bought, they sold, they planted, they built; 29.but on the day that Lot went out of Sodom it rained fire and brimstone from heaven and destroyed them all. 30.Even so will it be in the day when the Son of Man is revealed - Luke 17:24-30
And finally Christ mention the people those who are going to crucify him also "this generation".
O faithless and perverse generation
37.Now it happened on the next day, when they had come down from the mountain, that a great multitude met Him. 38.Suddenly a man from the multitude cried out, saying, “Teacher, I implore You, look on my son, for he is my only child. 39.And behold, a spirit seizes him, and he suddenly cries out; it convulses him so that he foams at the mouth; and it departs from him with great difficulty, bruising him. 40.So I implored Your disciples to cast it out, but they could not. 41.Then Jesus answered and said, O faithless and perverse generation, how long shall I be with you and bear with you? Bring your son here - Luke 9:37-41
And when the believers losing their faith on Christ, and trying to do the things with their own strength is also like crucifying Jesus Christ, and that was the reason Jesus Christ called those people as "O faithless and perverse generation".
Turn many of the children of Israel to the Lord their God
13.But the angel said to him, Do not be afraid, Zechariah, for your prayer has been heard, and your wife Elizabeth will bear you a son, and you shall call his name John. 14.And you will have joy and gladness, and many will rejoice at his birth, 15.for he will be great before the Lord. And he must not drink wine or strong drink, and he will be filled with the Holy Spirit, even from his mother's womb. 16.And he will turn many of the children of Israel to the Lord their God, 17.and he will go before him in the spirit and power of Elijah, to turn the hearts of the fathers to the children, and the disobedient to the wisdom of the just, to make ready for the Lord a people prepared - Luke 1:13-17
Even the calling of John the Baptist was to turn the children of Israel to Lord Jesus Christ, so we must lose our earthly identity to become a children of God.