In Catholic theology, Jesus’ death, when applied to a repentant individual, forgives such an individual of the **eternal **consequences of their sin. This being the case, I would ask your friend to demonstrate, rather than assert, why the removal of the **eternal **consequences of sin is not a good enough reason for Christ to offer Himself to the Father. In fact, that’s precisely what your friend probably believes Christ died to do. So, since he agrees with this part of the Catholic position, why is he arguing with it?
The second point is equivocation: they are using the object of forgiveness, of what is being forgiven, as if it can only have one sense … and then they are imposing this one sense onto Catholic theology in an effort to find inconsistency. But being forgiven of the eternal consequences of sin does not imply that one necessarily must be forgiven of the temporal consequences of sin by the same act.
Your friend asks why purification is necessary if Jesus died. Again … Jesus died so that we can be forgiven of the eternal consequences of our sin, i.e., so that we can live in friendship with God. Whether or not purification is needed even after the eternal consequences of sin are forgiven is not addressed by Jesus’ death. To claim otherwise by mere assertion is not to make a good argument, but is rather itself illogical insofar as it claims a non sequitur. (I would add that also that purification is only possible in light of the merit of Christ’s death.)
But your friend should also keep in mind that he probably agrees with aspects of the Catholic position on this point, too.
***Namely: Catholics and Protestants agree that no one in heaven is sinning, we will stop sinning when we go to heaven, and will be free of sin. But yet, we also agree that, before death, we will still be sinners. Catholics and Protestants disagree, however, on what they call that transition, and how to flesh it out theologically.
But in essence, they agree, and what we often do is not heed St. Paul’s warning in 2 Timothy 2:14: we quarrel about words when we often agree far more than we are willing to admit, and, simply for the sake of finding fault in each other, and in breaking down what the other believes, we insist on having fights***.