John Calvin on 2 Corinthians 11:18

18. Since many glory. The meaning is — Should any one say to me, by way of objection, that what I do is faulty, what then as to others? Are not they my leaders? Am I alone, or am I the first, in glorying according to the flesh? Why should that be reckoned praiseworthy in them, that is imputed to me as a fault?” So far then is Paul from ambition in recounting his own praises, that he is contented to be blamed on that account, provided he exposes the vanity of the false apostles.

To glory after the flesh, is to boast one’s self, rather in what has a tendency towards show, than in a good conscience. For the term flesh, here, has a reference to the world — when we seek after praise from outward masks, which have a showy appearance before the world, and are regarded as excellent. In place of this term he had a little before made use of the expression — in appearance. (2 Corinthians 10:7.)