“If we can in any way pay for our sins, Christs death was insufficient.”
1) Purgatory is NOT about any human person paying for his or her sins.
2) The existence of Purgatory in no way at all means Christ’s death was insufficient because it is precisely Christ’s death on the Cross and the grace won by it that powers the cleansing we call Purgatory or Final Theosis.
“The Catholic doctrine of purgatory is error, and a false gospel.”
No, the error is in your understanding. Maybe you should learn what Purgatory is before you post attacks getting it wrong.
Roman Catholic theology, for example, allows for prayers both to the dead and on behalf of them. But even Catholic authorities admit that there is no explicit authorization for prayers on behalf of the dead in the sixty-six books of canonical Scripture. Instead, they appeal to the Apocrypha (2 Maccabees 12:45), church tradition, the decree of the Council of Trent, etc., to defend the practice.
Your own catechism says "expiation" ...
III. THE FINAL PURIFICATION, OR PURGATORY
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1031 The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned.606 The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:607
1032 This teaching is also based on the practice of prayer for the dead, already mentioned in Sacred Scripture: "Therefore [Judas Maccabeus] made atonement for the dead, that they might be delivered from their sin."609 From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God.610 The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead: