We have not spoken properly in weeks because neither of us will be the one to give in first. I know it is ridiculous and I still cannot make myself move.

“A brother offended is harder to be won than a strong city: and their contentions are like the bars of a castle.”

The image is military. A brother offended is harder to win than a fortified city, and the contentions between them are like the bars of a castle gate. Proverbs is being realistic here rather than discouraging. Family and close friendship, because they had the least defence to begin with, build the thickest walls afterwards. Knowing how thick they are is what stops you expecting one casual text to swing the gate open.

“Let nothing be done through strife or vainglory; but in lowliness of mind let each esteem other better than themselves. Look not every man on his own things, but every man also on the things of others.”

Paul writes from prison to a church he loved, where two leaders had fallen out, and he grounds his answer in Christ, who did not cling to equality with God. Esteem the other person better than yourself, look after their interests alongside your own. In a standoff this is the only move that does not require the other person to go first. Somebody has to come down, and Paul says let it be you.