When is it appropriate to exhibit my "righteous anger"? We all seem to agree that anger in and of itself is not a sin, but rather what one does with it. But my experience is that the vast majority of Christians in my corner of the world these days react to even the smallest hint of anger as being "wrong", "unacceptable", etc. If you try to point out Jesus' anger when he cleaned out the temple, the typical response is, "Well, you're not Jesus."
First, Paul states he has been aggressive concerning "some points". Perhaps this indicates that when righteous anger is revealed, it is targeted against specific issues, not used as a weapon of mass destruction against the entire person. It seeks to correct the specific wrong, not condemn the whole person.
Secondly, Paul reminds us that authority comes inherent with one's calling, and that "to be a minister of Jesus Christ", to be "ministering as a priest", that it shouldn't be surprising that he has a responsibility and duty to provide instruction, even correction if needed. The salient thought is that the source of the anger is inspired by his calling, not his ego.
Thirdly, the goal "so that my offering of the Gentiles may become acceptable" indicates that his motivation is not to please himself, but to use righteous anger as a tool that makes the flock pleasing to God. (Ever seen a parent get "mad" at a child that nearly got themselves killed not looking both ways before crossing the street? Was the parent on a personal power trip? Was their anger justified?)
Finally, Paul identifies the true mark of righteous anger, that it acts as a part of the sanctification process of the Holy Spirit; sanctification being that something "defiled", "unclean" or "polluted" undergoes the necessary process to become spiritually clean and devoted entirely to God, not to EITHER the shepherd or the flock itself.†††