Paul could not bring himself to do anything that would harm the truth, even to vindicate himself. Promoting the truth (i.e, the gospel) was his great ambition even if it meant that some regarded him as a false apostle. This acting for the truth included judging the Corinthians if necessary ( 2 Corinthians 13:2). [source][source][source]
Context Summary
2 Corinthians 13:7-14 - How To Be Built Up
None can really injure the truth or stop its victorious progress. As well try to stop the sunrise. We often help others most in our weakness, because then we rely most on the Spirit of God. It is the noblest end of life to build up others through our own expenditure, even to the draining of our strength and resources. The world is apt at destruction; and indeed not much art is required for pulling down. But the divine work is to build; we have God's authority for that.
The valedictory address is very touching. Be perfected, 2 Corinthians 13:11, r.v., is really "be adjusted," "properly jointed," "articulated." God desires to set us as a skilful surgeon sets a dislocated limb. Let Him do it; let the Comforter comfort; let love and peace enter with the Holy Dove; and see that the inner atmosphere does not hinder the gracious healing work of the Spirit of God.
Note the threefold benediction, which maintains the doctrine of the Trinity, 2 Corinthians 13:14. The love of the Father is the fountain of all; the grace of the Lord Jesus is the channel for all; while the communion of the Holy Spirit brings us into partnership with the aims and resources of God. The salutation of the saints and the divine benediction are the worthy close of this noble letter [source]
Chapter Summary: 2 Corinthians 13
1Paul threatens severity, and the power of his apostleship, against obstinate sinners 5And, advising them to a trial of their faith, 7and to a reformation of their sins before his coming, 11he concludes his epistle with a general exhortation and a prayer
Greek Commentary for 2 Corinthians 13:8
Against the truth [κατα της αλητειας] He means in the long run. We can hinder and hold down the truth by evil deeds (Romans 1:18), but in the end the truth wins. [source]
For we can do nothing against the truth [] Your well doing is what we truly aim at. For, if we had any other aim, with a view to approving ourselves, we should fail, because we should be going in the face of the truth - the Gospel; and against that we are powerless. In that case we should be unapproved before God. [source]
What do the individual words in 2 Corinthians 13:8 mean?
Parse: Verb, Present Indicative Middle or Passive, 1st Person Plural
Root: δύναμαι
Sense: to be able, have power whether by virtue of one’s own ability and resources, or of a state of mind, or through favourable circumstances, or by permission of law or custom.
Greek Commentary for 2 Corinthians 13:8
He means in the long run. We can hinder and hold down the truth by evil deeds (Romans 1:18), but in the end the truth wins. [source]
Your well doing is what we truly aim at. For, if we had any other aim, with a view to approving ourselves, we should fail, because we should be going in the face of the truth - the Gospel; and against that we are powerless. In that case we should be unapproved before God. [source]