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.)

Seeing that many glory - The false teachers in Corinth. They boasted of their birth, rank, natural endowments, eloquence, etc.; see 2-Corinthians 11:22. Compare Philippians 3:3-4.
I will glory also - I also will boast of my endowments, which though somewhat different yet pertain in the main to the "flesh" also; see 2-Corinthians 11:23 ff. His endowments "in the flesh," or what he had to boast of pertaining to the flesh, related not so much to birth and rank, though not inferior to them in these, but to what the flesh had endured - to stripes and imprisonments, and hunger and peril. This is an exceedingly delicate and happy turn given to the whole subject.

Seeing that many glory after the flesh - Boast of external and secular things.

Seeing that many glory after the flesh,.... Or with respect to things external, such as their high birth and parentage, carnal descent, circumcision, learned education, and the like; of which the false apostles, being Jews, boasted, who it seems were many; and though a multitude is not to be followed to do evil, yet the apostle thought, that since there were so many who were indulged by this church in this way, he might be allowed to boast also of such like things, so far as he could with truth and a good conscience, and in order to secure some valuable ends:
I will glory also; for he was of the seed of Abraham as well as they, of the stock of Israel, and tribe of Benjamin, circumcised the eighth day, and brought up at the feet of Gamaliel; but these are not all the things he could, and would, and did glory of; he gloried of these, and of others besides them, which the false apostles could not, and thereby proved himself to be superior to them, even in external things, of which they bragged so much.

many--including the "false teachers."
after the flesh--as fleshly men are wont to boast, namely, of external advantages, as their birth, doings, &c. (compare 2-Corinthians 11:22).
I will glory also--that is, I also will boast of such fleshly advantages, to show you that even in these I am not their inferiors, and therefore ought not to be supplanted by them in your esteem; though these are not what I desire to glory in (2-Corinthians 10:17).

After the flesh - That is, in external things.