Purgatory is a doctrine of divine mercy. It is a recognition that most Christians are not so evil as to warrant hell and most are not yet perfected as to warrant immediate entrance into heaven. Purgatory makes perfect sense. Before looking at Scripture, let us look at our own lives first. Sin is a refusal to love God as I should.
Sin manifests an imperfect love.
Personal experience shows me that I am far from perfect in my love for God. As I understand sanctification, it is the recognition that we grow in holiness by the power of the Holy Spirit. But such an observation is in itself insufficient as grounds for its rejection. No where in Scripture are these terms used, yet you and I agree on all of them. The Scripture teaches each, not by name, but by meaning.