In American culture the topic of slavery is a delicate issue; because of the country's past enslavement of Africans there are tender emotions to this day.
Sadly, slavery was a fact of history for many cultures. At its height at least half of the population in Rome were slaves. Slavery was an inescapable fact of life for the Romans that Paul wrote to when he penned his theological apology (defense) of the gospel.
Paul used common metaphors of the day to drive home his point to his audience. Slavery was one of them. Consider his words:
"For sin will have no dominion over you, since you are not under law but under grace. What then? Are we to sin because we are not under law but under grace? By no means! Do you not know that if you present yourselves to anyone as obedient slaves, you are slaves of the one whom you obey, either of sin, which leads to death, or of obedience, which leads to righteousness? But thanks be to God, that you who were once slaves of sin have become obedient from the heart to the standard of teaching to which you were committed, and, having been set free from sin, have become slaves of righteousness. I am speaking in human terms, because of your natural limitations. For just as you once presented your members as slaves to impurity and to lawlessness leading to more lawlessness, so now present your members as slaves to righteousness leading to sanctification."
(Rom 6.14-19 ESV)
Since Paul already exhorted them to make a once-and-for-all surrender of themselves to God (Rom 6.13) he then explains the implications of such a conscecration: you consciously choose to become slaves to God.
In fact, Paul's point to the Romans is chilling; whether they surrender to God or not, they are already slaves to Someone or something, either God or sin.
Note the two options people have in slavery:
Slaves to Sin
slavery to sin whose end is death
slavery to impurity and to ever increasing lawlessness
Slaves to God
slavery to obedience whose end is righteousness
slavery to righteousness, which leads to sanctification
There's no way around it; you are a slaves to Somebody or something.
"When you were slaves of sin, you were free in regard to righteousness. But what fruit were you getting at that time from the things of which you are now ashamed? The end of those things is death. 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. For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord." (Rom 6.20-23 ESV)
What do you want? Do you want—
1. Slavery to sin → spiritual death → increased depravity → point-of-no-return spiritual death in hell
2. Slavery to God → righteousness → sanctification → eternal life in heaven
You have to choose one and there is no "Option 3"; which of the two do you choose?