Matt. 12:32 – Jesus says, “And anyone who says a word against the Son of man will be forgiven; but no one who speaks against the Holy Spirit will be forgiven either in this world or in the next.” Not forgiven in this age or the age to come.
What could be forgiven in heaven? or hell? Yet Jesus is implying that some sort of post-death forgiveness can occur for some sins, because He takes care to point out that it won't happen for the sin of speaking against the Holy Spirit.
1 Cor 3:10-15 According to the grace of God given to me, like a skilled master builder I laid a foundation, and another man is building upon it. Let each man take care how he builds upon it. 11 For no other foundation can any one lay than that which is laid, which is Jesus Christ. 12 Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, straw 13 each man's work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. 14 If the work which any man has built on the foundation survives, he will receive a reward. 15 If any man's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.
2 Tim 1:16-18 May the Lord grant mercy to the household of Onesiphorus, for he often refreshed me; he was not ashamed of my chains, 17 but when he arrived in Rome he searched for me eagerly and found me 18 may the Lord grant him to find mercy from the Lord on that Day and you well know all the service he rendered at Ephesus.
Onesiphorus is almost certainly dead, else why would Paul ask the Lord to grant mercy to his family apart from him? Yet Paul also asks the Lord to grant Onesiphorus mercy. If there is no Purgatory, why does Paul ask this? Those in hell cannot be helped by prayers and those in heaven have no need of prayers.
1 Pet 3:18-19 For Christ also died for sins once for all, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit; 19 in which he went and preached to the spirits in prison.
Mt 5:25-26 Make friends quickly with your accuser, while you are going with him to court, lest your accuser hand you over to the judge, and the judge to the guard, and you be put in prison; 26 truly, I say to you, you will never get out till you have paid the last penny.
In other words there is a temporal debt attached to all sin and if we haven't fully expiated that debt in this life we must do so in purgatory.
Lk 16:19-31 "There was a rich man, who was clothed in purple and fine linen and who feasted sumptuously every day. 20 And at his gate lay a poor man named Lazarus, full of sores, 21 who desired to be fed with what fell from the rich man's table; moreover the dogs came and licked his sores. 22 The poor man died and was carried by the angels to Abraham's bosom. The rich man also died and was buried; 23 and in Hades, being in torment, he lifted up his eyes, and saw Abraham far off and Lazarus in his bosom. 24 And he called out, 'Father Abraham, have mercy upon me, and send Lazarus to dip the end of his finger in water and cool my tongue; for I am in anguish in this flame.' 25 But Abraham said, 'Son, remember that you in your lifetime received your good things, and Lazarus in like manner evil things; but now he is comforted here, and you are in anguish. 26 And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.' 27 And he said, 'Then I beg you, father, to send him to my father's house, 28 for I have five brothers, so that he may warn them, lest they also come into this place of torment.' 29 But Abraham said, 'They have Moses and the prophets; let them hear them.' 30 And he said, 'No, father Abraham; but if some one goes to them from the dead, they will repent.' 31 He said to him, 'If they do not hear Moses and the prophets, neither will they be convinced if some one should rise from the dead.'"
God is love. Hell is being completely cut off from God. Hell is being completely cut off from love. In Hell, one can feel no love for anyone, not even one's self - it is total exclusion from love, from God. The rich man is clearly not in heaven, but he just as clearly feels compassion for his brothers and is concerned about their well-being, so he is clearly not in hell. Where is he? Incidentally, this is the only parable in which Christ gives one of the persons in the story a name - Lazarus. For this reason, many Christian commentators think this is not a parable, but a description of an historical event known to Christ.
Zech. 13:8-9 - God says 2/3 shall perish, and 1/3 shall be left alive, put into the fire, and refined like silver and tested like gold. The ones that perish go to hell, and there is no need for refinement in heaven, so those being refined are in purgatory. {This is very sobering. Two thirds of men will be eternally lost. It also agrees perfectly with the parable of the sower. In the parable of the sower only one third of the seed fell in rich soil and producted fruit.}
Wisdom 3:5-6 - Afflicted in few things, in many they shall be well rewarded: because God hath tried them, and found them worthy of himself.
As gold in the furnace he hath proved them, and as a victim of a holocaust he hath received them, and in time there shall be respect had to them.
Sirah 2:5 For gold and silver are tried in the fire, but acceptable men in the furnace of humiliation.
Rev 21:27 But nothing unclean shall enter it, nor any one who practices abomination or falsehood, but only those who are written in the Lamb's book of life.
Since nothing unclean can enter heaven that means that we must be completely cleansed from all faults and attachments to venial sin.
The doctrine of purgatory is not something that the Church made up, it is firmly rooted in sacred scripture. I've only posted a few scripture references for purgatory but there are many more. It is an article of faith that must be believed by all Catholics. Before the Protestant reformation all Christians believed in purgatory. Also Eastern Orthodox
Christians (while they don't believe in purgatory) believe that after death a soul in a state of grace must go through a purification process before being admitted into heaven. Since very few of us depart from this life perfect, most of us will end up having to go through purgatory.