Paul did not say, "Everything has a purpose." He did not say, "In spite of the difficult circumstances of me being in prison, God did something good." Paul simply did not make the best of a bad situation. What Paul said is far more remarkable.

He said, what has happened to me—that is, getting thrown into prison—has served to advance the good news. In other words, what has happened to me, the sufferings I am enduring, unjust as they are, have opened up an opportunity for the good news of Jesus' resurrection and new life to advance. And if I hadn't been put in this prison, this might not have happened. It's a remarkable recognition of God's bigness over his troubles.

This is not an "in spite of" perspective. It's a "because of" perspective. You see, Paul has this gigantic view of God. A really big view of God. And he knows that God is always at work bringing forth His Kingdom purposes, and nothing can stop God's unfolding plan.