William Burkitt on 2 Corinthians 10:3

That is, "Although I yet dwell in the body, and consequently am not free from human infirmities and weaknesses; yet neither my ministry nor my life are from fleshly principles, by fleshly means, or fleshly ends." The best and holiest of men in this life walk in the flesh; they are clothed with a mortal body, but they do not war after the flesh, they do not fight under the banner of corrupt nature.

Here note, The Christian life described; it is a warfare; we war; It is a life of vigorous opposition. The Christian has many enemies to conflict with, and to contend against, both outward and inward enemies; in a passive sense, he is a man of strife and contention, his hand is against many, and many hands against him; he doth not manage a war for the flesh, but against the flesh: And in the next verse, he tells us with what weapons he managed this war.