For we -- Some manuscripts read For you.
do not wrestle -- The Greek word used here - πάλη palē - denotes a “wrestling;” the use of hand-to-hand combat. Then by extension it came to mean a struggle, fight, combat. Here it refers to the struggle or combat of the Christian against evil forces.
Wrestling features trickery and deception, like Satan and his hosts when they attack.
against flesh and blood -- cf. 2 Corinthians 10:3-5. The opposition Christians face comes from the unseen world of spiritual evil, and Christ has authority over that realm (see Ephesians 1:21-22).
It is interesting that the literal Greek order in this occurrence is “blood and flesh”; but English usage reverses the order and makes it coincide with the Greek order of the words in Matthew 16:17; 1 Corinthians 15:50; Galatians 1:16; Hebrews 2:14.
The Christian life is a spiritual battle in which the ultimate opposition to the gospel stems from evil spiritual powers (cf. Ephesians 1:21; Ephesians 3:10 and notes). These powers can operate through humans (Ephesians 4:14; Ephesians 4:27) and institutions, but they cannot be reduced solely to these manifestations. - NIVBTSB
The apostles does not mean to imply that Christians have no enemies among men that oppose them. They are exposed to persecution, false teachers, etc., but behind these evil forces are lurking invisible spirits of wickedness that seek to destroy them.
the rulers [principalities] -- This word refers to principal rulers or chieftains. αρχας G746.
These various terms show the diversity and comprehensiveness of the enemy’s power, reminding us that the battle cannot be fought merely with human resources.
The 4 designations describe the different strata and ranking of those demons and the evil supernatural empire in which they operate. Satan’s forces of darkness are highly structured for the most destructive purposes. Cf. Colossians 2:15; 1 Peter 3:22.
against the authorities -- εξουσιας G1849, refers to those who have "power" or "authority" in their realm of influence. The "Leaders".
against the cosmic powers -- κοσμοκρατορας, G2888, the Lord, or ruler, of his world. The ruler who presides over, as seen in the next phrase, "this present darkness" or "this world of darkness" and thus to mean a world of sin and evil.
over this present darkness -- Darkness here is an emblem of ignorance, misery, and sin. It accurately pictures these malignant spirits as ruling over a dark world. The earth-- dark and wretched and ignorant and sinful.
against the spiritual forces of evil -- Literally, "the spiritual things wickedness."
forces of wickedness -- Refers to hostile supernatural entities. Because of Christ’s victory over the evil powers, believers have courage and strength to resist them (Ephesians 1:19-21; Ephesians 3:10; Colossians 2:15).
in the heavenly [high] places -- “in celestial or heavenly places.” As in Ephesians 1:3; eph 3:10, this refers to the entire realm of spiritual beings.
The word (ἐπουράνιος epouranios) is used of those that dwell in heaven, Matthew 18:35; Philippians 2:10; of those who come from heaven, 1 Corinthians 15:48; Philippians 3:21; of the heavenly bodies, 1 Corinthians 15:40. Then the neuter plural of the word is used to denote the heavens; and then the “lower” heavens, the sky, the air, represented as the seat of evil spirits. (BN)