This psalm forms a chiastic structure:
1a) Psa 75:1-7, Thanksgiving + judgment of wicked + exaltation;
1) Psa 75:1, We give thanks to You, O God, for Your wondrous works declare Your name is near;
2) Psa 75:2-5, I will judge uprightly + Boastful, do not lift up your horn on high;
3) Psa 75:6-7, God is the judge who puts down one and exalts another;
central axis) Psa 75:8, “For in the hand of the LORD there is a cup, and the wine is red; it is fully mixed, and He pours it out; surely its dregs shall all the wicked of the earth drain and drink down;
2a) Psa 75:9-10, Praise + judgment of wicked + exaltation of righteous;
1) Psa 75:9, I will declare forever and sing praises to the God of Jacob;
2) Psa 75:10a, All the horns of the wicked I will also cut off;
3) Psa 75:10b, But the horns of the righteous shall be exalted.
A “horn” as it is used here and elsewhere in Psalms, is defined in Strong’s as referring to the strength or might of the wicked. Matthew Henry’s Commentary tells us that “horn” refers to power or authority; i.e., the wicked lifts up his own horn, his own authority, in defiance and rebellion against the Lord’s authority over him. Smith’s Bible Dictionary says “horn” is often used metaphorically to signify strength and honor, because horns are the chief weapons and ornaments of the animals which possess them. Also, that they can signify victory, supreme authority, thus concretely, kings or kingdoms. The use of “horn” to mean strength, power, or authority is continued throughout the Psalms.
The matching pairs or elements of this psalm teaches us, that God is the One who brings one down and another up. In fact, He will bring the horn of the wicked down, cutting them off completely, or removing their power, might, and authority from them. And He will bring the righteous up, or increasing their power, might, and authority. In this He is the Just Judge, because all of His judgments are upright.
Sometimes things that seem unfair to us, only seem that way because we live immersed in a culture which praises evil and punishes good, exactly the opposite that God established governments for in the first place (Rom 13:3-4). In determining what is truly just and upright, we must at all times take Torah as our plumb line of righteousness, which remains true in a crooked and twisted world.