A.T. Robertson Commentary 2 Corinthians 10:3

"For though we walk in the flesh, we do not war according to the flesh" — 2 Corinthians 10:3 (ASV)

In the flesh (εν σαρκ). But that is a very different thing from walking κατα σαρκα according to the standards of the flesh as his enemies charged. It is easy enough to make insinuations.

We war (στρατευομεθα). Literary plural again after λογιζομα in verse 2. Old word to lead an army (στρατος). In N.T. only in the middle as here. Paul admits that he fights, but only the devil and his agents even if wearing the livery of heaven. Paul knew the Roman army well. He knows how to use the military metaphor.