Faith is God’s sovereign gift, and God has decided to withhold it from the non-elect, but instead he chooses to harden them; therefore, to offer salvation to the non-elect as if God desires them to be saved and as if it is possible for them to be saved would be to lie to them in God’s name. There is no offer of salvation to the non-elect, but only a command that they can never obey, and God will punish them with hellfire.
This does not prevent us from preaching the gospel to all men, since it is not our duty or right to pick out the elect and preach only to them, or to pick out the non-elect and exclude them. The point is that we must not present the gospel as a sincere offer to all, as if God’s “desire” can differ from his decree, as if God could or would decree against his “desire,” and as if it is possible for even the non-elect to be saved.
God loves the elect and desires (and thus has decreed) their salvation; he hates the reprobates and desires (and thus has decreed) their damnation (Romans 9:13). The preaching of the gospel must be consistent with this. So we must present the gospel as a serious command to all, as if it is required of all to believe (Acts 17:30), and as if God intends to summon the elect and harden the non-elect by the same preaching of the gospel (2 Corinthians 2:15-16).
Thus we must preach the gospel to all men for at least three reasons: 1. God commands us to preach the gospel to all people, 2. We do not know and should not consider beforehand who are the elect and who are the reprobates, and 3. The purpose of preaching the gospel is not only to summon the elect to faith, but also to harden the reprobates in their unbelief.