Satan was, according to the temptation narrative in the synoptics, trying to entice Jesus with the promise of
social dominance over others by means of political power.
In the Old Testament, Gideon was offered the same in a more limited sense (i.e. over Israel) but rejected the offer because he believed that God was the only true sovereign:
22 Then the Israelites said to Gideon, “Rule over us, you and your son and your grandson also; for you have delivered us out of the hand of Midian.” 23 Gideon said to them, “I will not rule over you, and my son will not rule over you; the Lord will rule over you.” (Judges 8:22-23)
This is important since, in the beginning, God intended humankind to exercise stewardship only over animals and the environment but not to have dominance over our fellow human beings. As the Jesuit theologian Francisco Suarez stated in 1613:
"men are by nature free and subject to no one" (DL 3.1.1). He furthermore wrote:
Selections from Three Works - Online Library of Liberty
9. Besides this truth can be taken from the holy Fathers, first, because they assert that man was created by God free and free-born, and only received directly from God the power of ruling over the brute beasts and inferior things; but the dominion of men over men was introduced by human will through sin or some adversity. This Ambrose hands down on Colossians 3, at the end; and more broadly Augustine, 19, The City of God, ch.15, and bk. Quaestion. in Gen. q.153, and Gregory bk.21, Moralia, ch.10, elsewhere ch.11, and in Pastorali, p.2, ch.6.
The urge to have exploitative power over and higher status than other individuals, is associated in the church's tradition with the devil and the first sin:
"Who does not know that kings and dukes had their rulership from those who, not knowing God, strove from blind greed and intolerable presumption to dominate their equals, namely mankind, by pride, rapine, perfidy, murder, and crimes of all sorts, urged on by the ruler of the world, i.e., the devil?…
For His Son (Jesus), even as He is undoubtingly believed to be God and man despised a secular kingdom, which makes the sons of this world swell with pride, and came of His own will to the priesthood of the cross…
Therefore all Christians who desire to reign with Christ should be warned not to strive to rule through ambition of worldly power…"
(Pope Gregory VII in 1081: 552; see also Poole 1920: 201, fn. 5)
As Jesus himself taught:
25 But Jesus called them to Himself and said, “You know that among the Gentiles, those who appear to be their kings lord it over them, and their 'great' men are tyrants over them. 26 But it shall not be this way among you, rather whoever wishes to become great among you shall be your servant, 27and whoever wishes to be first among you shall be your slave; 28 just as the Son of Man did not come to be served, but to serve, and to give His life a ransom for many.” (Matthew 20:25-28)
So, Jesus was made to pass through this temptation first and he prevailed.