It’s a mirror image of God’s authority. We are adopted by the Father. Not slaves. That’s the theology of Islam, not Christianity.
The scriptures use many different analogies to describe God's relationship to us: Husband-wives, Father-son, God-Christ, Arborist-vine, Shepard-Sheep, General-Soldier, King-Servant, and yes Master-Slave. As Paul explains in Romans 6:
15What then? Shall we sin because we are not under law but under grace? Certainly not! 16Do you not know that to whom you present yourselves slaves to obey, you are that one’s slaves whom you obey, whether of sin leading to death, or of obedience leading to righteousness? 17But God be thanked that though you were slaves of sin, yet you obeyed from the heart that form of doctrine to which you were [e]delivered. 18And having been set free from sin, you became slaves of righteousness. 19I speak in human terms because of the weakness of your flesh. For just as you presented your members as slaves of uncleanness, and of lawlessness leading to more lawlessness, so now present your members as slaves of righteousness [f]for holiness.
20For when you were slaves of sin, you were free in regard to righteousness. 21What fruit did you have then in the things of which you are now ashamed? For the end of those things is death. 22But now having been set free from sin, and having become slaves of God, you have your fruit [g]to holiness, and the end, everlasting life. 23For the wages of sin is death, but the [h]gift of God is eternal life in Christ Jesus our Lord.
We are literally slaves of God. Just as those not submitted to Christ find themselves drawn about by sin and pay the penalty thereof. We were purchased at the cost of Christ's blood. Our enslavement to Him is as real as His sacrifice. And like a slave we no longer do our own will but the will of Christ:
Take Up Your Cross
(Matthew 10:37-39; Matthew 16:24-28; Mark 8:34-38)
23And he said unto all, If any man would come after me, let him deny himself, and take up his cross daily, and follow me. 24For whosoever would save his life shall lose it; but whosoever shall lose his life for my sake, the same shall save it. 25For what is a man profited, if he gain the whole world, and lose or forfeit his own self? 26For whosoever shall be ashamed of me and of my words, of him shall the Son of man be ashamed, when he cometh in his own glory, and the glory of the Father, and of the holy angels. 27But I tell you of a truth, There are some of them that stand here, who shall in no wise taste of death, till they see the kingdom of God.
All who wear the name of Christ are chatel of God. How He directs us is His business. And when we obey those God has put in authority over us it is as if we are obeying God. The same holds true whether that is to an employer, a parent, or a husband. There is no option to rule ourselves, God merely directs that obedience owed Him towards others. As Paul explained to the Colossians:
Slaves, obey your earthly masters in everything, not only to please them while they are watching, but with sincerity of heart and fear of the Lord.
23Whatever you do, work at it with your whole being, for the Lord and not for men, 24because you know that you will receive an inheritance from the Lord as your reward. It is the Lord Christ you are serving.