Adam Clarke on 2 Corinthians 10:4

The weapons of our warfare - The apostle often uses the metaphor of a warfare to represent the life and trials of a Christian minister. See Eph 6:10-17; 1Tim 1:18; 2Tim 2:3-5.

Are not carnal - Here he refers to the means used by the false apostle in order to secure his party; he calumniated St. Paul, traduced the truth, preached false and licentious doctrines, and supported these with sophistical reasonings.

But mighty through God - Our doctrines are true and pure, they come from God and lead to him, and he accompanies them with his mighty power to the hearts of those who hear them; and the strong holds - the apparently solid and cogent reasoning of the philosophers, we, by these doctrines, pull down; and thus the fortifications of heathenism are destroyed, and the cause of Christ triumphs wherever we come; and we put to flight the armies of the aliens.