I never claimed that "Calvinism says a person is a slave to sin". But I did quote God's Word, because God said it before John Calvin.
You seem to have overlooked or ignored the fact that everyone is born into slavery to sin and Satan. So you're half right, in saying - "A person cannot meaningfully be enslaved to himself, because slavery requires an external master." Satan is that external master that you mentioned.
Adam was not inherently sinful, nor was he "forced" to sin by an already present corrupted nature. The sin nature (total depravity) is a consequence of the Fall, not a pre-existing condition. After his transgression, that original liberty was lost, leaving humanity with a corrupted nature that inclines only toward sin.
The natural man sins "voluntarily" because it is the overflow of his corrupt desires. He cannot choose spiritual good because he lacks the inclination or desire to do so. Jesus states, "Everyone who commits sin is a slave to sin" (John 8:34). The Apostle Paul explains this condition by stating the "mind set on the flesh is hostile to God" (Romans 8:7)
While man’s sin is internal, the external realm of the unsaved is ruled by Satan, whom Scripture describes as the "ruler of this world". The devil does not necessarily need to physically force the natural man to do his bidding; rather, he exploits humanity's innate love for sin, leading unbelievers to do his will.
Paul refers to unbelievers as those who are "held captive by him [the devil] to do his will" (2 Timothy 2:26).
