What does Proverbs 12:16 mean?

The prior verse (Proverbs 12:15) spoke of a "fool" as a person who is hard-headed, or stubborn, or resistant to advice. When such a person is annoyed, perhaps by a sharp disagreement or an insult, he loses control and shows his anger. In contrast, a wise person stays calm under similar circumstances. There's a strange contradiction in the life of someone who strongly resists correction (Proverbs 1:7) yet succumbs quickly to their own frustration. Then again, both problems have the same root cause: selfish arrogance.

A wise person controls his emotions. He does not fly off the handle at the slightest provocation. He manifests self-control, which is produced by the Holy Spirit (Galatians 5:22–23). The apostle Peter reminds us that Jesus did not revile in return when He was reviled. Neither did He threaten others when He suffered. Instead, He "continued entrusting himself to him who judges justly" (1 Peter 2:23). In 1 Peter 3:9–11, Peter writes: "Do not repay evil for evil or reviling for reviling…'whoever desires to love life and see good days, let him keep his tongue from evil and his lips from speaking deceit; let him turn away from evil and do good; let him seek peace and pursue it.'" It is a mark of godliness to remain calm when circumstances or mean-spirited people annoy us.