Jamieson, Fausset and Brown on 2 Corinthians 11:18

18. 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 2Co 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 (2Co 10:17).