This is where Chris Matthew answers my friend’s question in regards to the relationship between the offer of the gospel and Calvinism:
If limited atonement is true we find ourselves with a bit of a problem. Christ commands people to believe the gospel that haven’t had their sins forgiven. In fact, it isn’t possible for them to have their sins forgiven and it is false that their sins are forgiven. So, that would entail that God commands them to believe something that is false.
The apparent problem is easily resolved if we clarify the propositions involved in Gospel acceptance. Perhaps it’s something like,
(G) Christ died for your sins. If you believe, your sins are forgiven.
Nowhere in the Scriptures are we taught that the sins of the elect have been forgiven from eternity. The elect are justified and sanctified in time. Thus, Christ commands all people (elect or not) to believe the Gospel. If so, there is no difficulty here. Limited atonement states that G will only be accepted by the elect ─ such that the elect’s acceptance is a contextual fact, not a proposition inherent in the Gospel message itself. Nothing here is “false.”