Albert Barnes on 1 Corinthians 16:21

The salutation of me Paul with mine own hand. It is evident that Paul was accustomed to employ an amanuensis in penning his epistles, Rom 16:22 though he signed his own name, and expressed his Christian salutation in every epistle, 2Thes 3:17, Col 4:18. This gave a sanction to what was written; was a proof that it was his own, and was a valuable token of affectionate regard. It was a proof that there was no fraud or imposition. Why he employed an amanuensis is not known.