Correct; because Christ purchased salvation for us it is a free gift, but that doesn't exclude the ability to reject that gift. Your reasoning simply doesn't stand up to scripture, because we see that people can deny the Christ that bought them.
"But false prophets also arose among the people, just as there will also be false teachers among you, who will secretly introduce destructive heresies, even denying the Master who bought them, bringing swift destruction upon themselves" (2 Peter 2:1).
Since Peter is describing those who are not saved, being "bought" by the Master cannot be referring to what happened at Calvary. Peter was writing to the Jews, most of whom considered themselves as children of God. However, we know from scripture that many who believed they were among the righteous, like the Pharisees, were not.
Look at it this way: If Christ purchased salvation for all, then why would anyone go to hell? Is it because Christ's blood covers all sin except the sin of rejecting the gospel? If that is so, then obviously his sacrifice was insufficient.
God is nothing if not just, and if Jesus did indeed pay for the sins of all, then it would be unjust for God to impose a second punishment on those whose sins were covered the first time. Either Christ's sacrifice is sufficient or it isn't. Calvinism holds that his punishment in our place meets God's requirement of a blood sacrifice for the sins of the elect.
How many sins did Christ pay for? If for all, why would anyone go to Hell? For what sin would be be being punished? For unbelief? Is that not a sin? Is that the sin Christ didn't die for?
Think it through.
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