"There will be neither sin nor attachment to sin in heaven. We (at least most of us) are still sinning and are attached to sin at the end of this life. Therefore there must be a period between death and heavenly glory in which the saved are cleansed of sin and their attachment to sin."
The underlying problem with such reasoning is that it completely ignores a quintessential truth of the gospel, namely that our Lord Jesus Christ paid the full penalty for our sin via atonement on the cross at Calvary. In other words, He has already accomplished purification for sin on our behalf. Christ is the one and only remedy for the problem of sin. He is our Purgatory. We are made complete in Him. His expiatory work is absolutely sufficient in itself. He cleanses us from every sin. God does not impute sin to believers. He does not count sin against those who have been forgiven in His sight. The blood of Christ is applied to believers by faith:
"By this will we have been sanctified through the offering of the body of Jesus Christ once for all. Every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins; but He, having offered one sacrifice for sins for all time, sat down at the right hand of God, waiting from that time onward until His enemies be made a footstool for His feet. For by one offering He has perfected for all time those who are sanctified." (Hebrews 10:10-14)
If we truly must make amends for any of the sins that we have committed in this lifetime, then how does it not follow that Christ's work was insufficient to atone for our sins? How is that the forgiveness of sin? The Scriptures clearly teach justification by faith, apart from the merit of all good works:
"For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast." (Ephesians 2:8-9)
Jesus Christ once said of His atonement sacrifice, "It is finished" (John 19:30). This utterance certainly bears significance, considering that the Greek word for this phrase is tetelestai. During New Testament times, this message would be imprinted on business records and receipts whenever a transaction would be completed successfully. The Greek term tetelestai simply indicates the full payment of a bill. Respectively, that is what Jesus affirmed regarding the completion of His earthly mission. He paid our sin debt in full, thereby enabling us to enter directly into the Father's presence.
It is impossible for man to make reparation for sin, not even an iota. We are forgiven by Christ's wounds and not anything done on our part (1 Peter 2:24). It is solely by the grace of God that we can be saved from eternal condemnation. Thus, the Roman Catholic doctrine of purgatory utterly misunderstands the nature of the biblical atonement. It would be an offense to the utmost for us to try to pay back a debt that God Himself has already paid in full. The necessity of purgatory can only make sense in a works-based justification theological framework, which is flatly contradicted by Scripture.
The reasoning comprising the logical syllogism employed by Catholic Answers is deceptive at best. It is highly fallacious, for it draws a conclusion that simply does not follow from the two mentioned premises. This is known as a non-sequitur. Catholic Answers presents to unsuspecting readers a false dichotomy, assuming that purgatory must be the only logical conclusion. But that is simply not true. The idea does not even have scriptural backing. The blood of Christ cleanses believers from all sin. Purgatory is a perfect example of philosophy gone wrong:
"See to it that no one takes you captive through philosophy and empty deception, according to the tradition of men, according to the elementary principles of the world, rather than according to Christ." (Colossians 2:8)