"The big switch" is a switch from a slave of sin to a slave of God and righteousness.
Paul in Romans 6 made it crystal clear.
"What then are we to sin because we are not under law but under grace? By no means! [notice the exclamation point] Do you not know that if you present yourselves to anyone as obedient slaves, you are slaves to the one whom you obey, either of sin, which leads to death [spiritual damnation], or of obedience which leads to righteousness?... 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....But now that you have been set free from sin and have become slaves to God, the fruit you get leads to sanctification and it's end, eternal life." Romans 6:15-16, 19, 22