I believe the source of the doctrine that we ought to regard ourselves as sons and not slaves comes from a misreading of Galatians 4 and Romans 8. Galatians 4:6-7 says:
And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” So you are no longer a slave, but a son, and if a son, then an heir through God.
And Romans 8:14-16 says:
For all who are led by the Spirit of God are sons of God. For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” The Spirit himself bears witness with our spirit that we are children of God.
There it is. The Bible explicitly affirms that we are "no longer slaves" and that we did not receive the "spirit of slavery". Instead, we are offspring: we are children who call God "Abba! Father!" How clear can that be? And who am I to re-introduce the idea of "slavery to God" when Scripture has abolished it?
The answer lies in the context. It is a matter of what (or Whom) you are a slave to.
Romans 8:15 says that we are not to be slaves to fear. Literally in the Greek, "You have not received a spirit of slavery unto fear again." Galatians 4:3 says we are no longer slaves to the elemental spiritual forces of the world. (A few verses later in Galatians 4:9 Paul asks, "Why are you turning back to those weak and miserable spiritual forces? Do you wish to be enslaved by them all over again?"). And in Romans 6:17-18 Paul writes that we are not to be slaves to sin: "though you used to be slaves to sin...you have been set free from sin and have become slaves to righteousness."
So some kinds of slavery are bad: slavery to sin, to fear, and to elemental spiritual forces. But some kinds of slavery are good. Paul speaks highly of slavery to obedience in Romans 8:16 and slavery to righteousness in Romans 8:18.
What about slavery to God? Is that a good thing or a bad thing?
It is very, very good. In Romans 6:22 Paul writes: "But now that you have been set free from sin and have become slaves of God, the fruit you get leads to sanctification and its end, eternal life."
Paul called himself a slave of God repeatedly, using the Greek word doulos. See for example Romans 1:1: "Paul, a slave of Christ Jesus, called to be an apostle and set apart for the gospel of God—". See also Galatians 1:10, Philippians 1:1, and Titus 1:1. (The Greek word doulos is often translated as "servant". But my Greek professor Murray Harris was surely right to insist that the correct translation is "slave". In English, a "servant" is someone who works for hire and is free to quit whenever he pleases and go work for someone else. A doulos had no such freedom. A doulos was bound to his master.)
Paul was not alone describing himself as a slave of Christ. James calls himself "a slave of God and of the Lord Jesus Christ" (James 1:1). Jude likewise opens his epistle with, "Jude, a slave of Jesus Christ" (Jude 1:1). John writes that God sent his angel to "his slave John" (Revelation 1:1).
Nor was the term "slave of God" (or "slave of Christ") simply a self-designation. Paul calls Epaphras "a slave of Christ Jesus" in Colossians 4:12. Peter instructs his readers to "live as God's slaves" (1 Peter 2:16). Paul affirms in 1 Corinthians 7:22 that a Christian who is politically free is nevertheless "a slave of Christ".
We can go further. Jesus insists that his disciples regard themselves as slaves of God even when they have been perfectly obedient: "So you also, when you have done all that you were commanded, say, ‘We are unworthy slaves; we have only done our duty.’" (Luke 17:10).
In a moving example of submission to God's will, the young virgin Mary responds to Gabriel's message in Luke 1:38 with, "I am the slave [Greek doule, feminine doulos] of the Lord; let it be to me according to your word.” The angel does not correct her. He does not say, "Mary! You're not a doule of the Lord - you're a thugater [daughter] of the Lord!" Mary had chosen the right word and had the right self-perception. What was right for Mary is right for us. We anticipate the day when, by God's grace, we will hear for ourselves the words he will say to every obedient subject: "Well done, good and faithful slave" (Matthew 25:23).
But how is our status of slavery to be reconciled with our status of sonship? Because indeed there are plenty of Bible verses that affirm us as sons and daughters of God. John 1:11: "To all who did receive him, to those who believed in his name, he gave the right to become children of God." 1 John 3:1: "See what great love the Father has lavished on us, that we should be called children of God."
The simple answer is that no reconciliation is necessary because we have dual status. We are both sons and slaves. It is comparable to the dual nature of Christ: he is both human and divine, and neither of his two natures negates or nullifies the other. Christian orthodoxy does not permit us to say, "Jesus isn't God, he's human", or, "Jesus isn't human, he's God." He's both, and Christians have been comfortable affirming his two natures for 2000 years.
So also must we be comfortable affirming our two natures as children of God and slaves of God. These two natures manifest themselves in two of the most common biblical words we use for Deity: "Father" and "Lord". We call him Father because we are his offspring, and we call him Lord ("Master") because we are his slaves. The Christian disciple utters no contradiction and feels no tension when he says, "God is my Master and I fear him, and he is my Father and I love him. He commands me as his slave, and he loves me as his son."
The danger of Keller's rhetorical question is that it invites us to smother our identity as slave with the pillow of our identity as son. "Child" and "slave" are set in opposition to each other, and it is urged upon us as a spiritual duty to make sure that "child" wins. I deny that this approach is biblical or helpful. When Keller asks, "In all that I do, am I acting like a slave who is afraid of God, or like a child who is assured of my Father's love?", I answer, "Both!" Jesus commands me to call myself a slave in Luke 17:10, and he commands me to be afraid of God in Luke 12:5 ("But I will show you whom you should fear: Fear him who, after your body has been killed, has authority to throw you into hell. Yes, I tell you, fear him.") This fearful respect for God and humble self-regard as his slave lives side-by-side in the mind of the mature believer with a shining love for God and an exultant delight in being his child.
I think you will find that circumstances often dictate the appropriate mode of relating to God on any particular day. When life presents you with temptations to defy the will of God - to rebel, in attitude or action, against that which he has ordained - then it is good to think, following the example of the Virgin Mary, "I am the Lord's slave. I will do as he says, and I will accept what he gives." But when life grieves you with doubt and challenges you to despair, then it is good to think, "By his grace alone I am still a child of God. He loves me."
