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 the sins of mankind? How is that the forgiveness of sin? The Scriptures clearly teach justification by faith, apart from the merit of all 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)
Our Lord Jesus Christ once said of His atonement sacrifice, "It is finished" (John 19:30). This utterance certainly must bear 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. We can neither compliment nor supplement what He has accomplished on our behalf. We are healed by Christ's wounds. 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 can only make sense in a works-based justification theological framework, which is flatly contradicted by Scripture.
The Parable of the Rich Man and Lazarus presents to us a handful of insights as to what happens to souls in the afterlife (Luke 16:19-31). Lazarus immediately entered Abraham's bosom upon death, whereas the rich man woke up in torment of at his appointed hour. Upon pleading for water to sooth his pain and begging to be resurrected from the grave to warn relatives of their upcoming spiritual fate, the rich man was denied access. There also exists a great chasm that cannot be crossed (Luke 16:26). Hence, we learn that the moment of physical death seals our eternal destiny. There are no chances to receive God's forgiveness after death. Either heaven or hell will be the set eternal destiny of every person, according to Scripture. It mentions no third place for souls to enter after death for a time of purification. Interestingly, our Lord Jesus Christ made no mention of purgatory to the repentant thief on the cross (Luke 23:39-43).
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. This 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)