[Try again. Catholicism never defined what exactly goes on in purgatory so this is nothing but attacking a strawman.]
From New Advent the Roman Catholic Encyclopedia -
I. CATHOLIC DOCTRINE
Purgatory (Lat., "purgare", to make clean, to purify) in accordance with Catholic teaching is a place or condition of temporal punishment for those who, departing this life in God's grace, are, not entirely free from venial faults, or have not fully paid the satisfaction due to their transgressions. The faith of the Church concerning purgatory is clearly expressed in the Decree of Union drawn up by the Council of Florence (Mansi, t. XXXI, col. 1031), and in the decree of the Council of Trent which (Sess. XXV) defined: "Whereas the Catholic Church, instructed by the Holy Ghost, has from the Sacred Scriptures and the ancient tradition of the Fathers taught in Councils and very recently in this Ecumenical synod (Sess. VI, cap. XXX; Sess. XXII cap.ii, iii) that there is a purgatory, and that the souls therein are helped by the suffrages of the faithful, but principally by the acceptable Sacrifice of the Altar; the Holy Synod enjoins on the Bishops that they diligently endeavor to have the sound doctrine of the Fathers in Councils regarding purgatory everywhere taught and preached, held and believed by the faithful" (Denzinger, "Enchiridon", 983). Further than this the definitions of the Church do not go, but the tradition of the Fathers and the Schoolmen must be consulted to explain the teachings of the councils, and to make clear the belief and the practices of the faithful.
That temporal punishment is due to sin, even after the sin itself has been pardoned by God, is clearly the teaching of Scripture. God indeed brought man out of his first disobedience and gave him power to govern all things (Wis. x, 2), but still condemned him "to eat his bread in the sweat of his brow" until he returned unto dust. God forgave the incredulity of Moses and Aaron, but in punishment kept them from the "land of promise" (Num., xx, 12). The Lord took away the sin of David, but the life of the child was forfeited because David had made God's enemies blaspheme His Holy Name (II Kings, xii, 13, 14). In the New Testament as well as in the Old, almsgiving and fasting, and in general penitential acts are the real fruits of repentance (Matt., iii, 8; Luke, xvii, 3; iii, 3). The whole penitential system of the Church testifies that the voluntary assumption of penitential works has always been part of true repentance and the Council of Trent (Sess. XIV, can. xi) reminds the faithful that God does not always remit the whole punishment due to sin together with the guilt. God requires satisfaction, and will punish sin, and this doctrine involves as its necessary consequence a belief that the sinner failing to do penance in this life may be punished in another world, and so not be cast off eternally from God.