The well-meant offer [WMO] notion is not a faithful representation of the Bible, but is a bastardization of the Reformed faith. Here are several reasons why Christians should reject this deformed position that is popularly held by moderate Calvinists, Arminians and Amyraldians:
The WMO is contradictory because it teaches that God decreed the reprobate for perdition, but still desires to save them.
The WMO impugns the righteous character of God by arguing that He loves workers of iniquity, while the Bible teaches that God’s eyes are too pure to behold evil that He cannot “look on iniquity” (Hab. 1:13).
The WMO is denigrating to God’s immutability because it teaches that Yahweh has a loving disposition for the reprobate in this life, but has an unremitting hatred for them in hell.
The WMO is an attack on the doctrine of simplicity because it teaches that God has two wills—a will of decree and a will of desire—which are both in opposition to each other. Therefore, based on the WMO notion, God is not sovereign; He is schizophrenic.
The WMO is not Reformed theology; it is deformed thinking. Historically, WMO teachers have twisted doctrines like grace and love and applied them to reprobates. However, the Bible teaches that God’s grace and love are reserved exclusively for the elect. The WMO teaches that God loves everyone, but the Bible teaches that God hates the wicked (Ps. 5:5).
WMO teachers say that God provides a non-salvific type of common grace and love to reprobates, but they cannot explicitly show where the words grace or love in the Bible are applied to reprobates. That’s because anytime God’s grace and love are mentioned in Scripture, they are always characterized as being salvific, eternal, and immutable.
WMO theoreticians will slavishly argue that Matthew 5:45 ("sun rise on the evil and on the good, and sends rain on the just and on the unjust") is proof that God provides a non-salvific type of love and grace to even reprobates. But Matthew 5:45 doesn’t even mention God’s grace or love, nor does it mention anything about God desiring to save reprobates.
The Bible does not teach that God is sincerely offering salvation to reprobates, nor does it teach that Christ purchased salvation for reprobates. Christ died and purchased salvation for only the elect. However, the Bible makes it patently clear that Christians must indiscriminately preach the true gospel of Jesus Christ to all men without exception.
 Sure, rain and sunshine are particular aspects of God’s providence. But Matthew 5:43-48 says nothing about God pouring out His overtures of grace upon reprobates, and it says nothing about particular aspects of God’s love in this life for all without exception. The reference to rain and sunshine does not deduce that God is bestowing love or pouring out grace. If it thunders outside, does this mean that God hates everyone in the whole world? Of course not. There is nothing common about grace. Again, every time God's grace is mentioned in Scripture, it is always salvific in its character. Therefore, when men argue that grace is common, they are injecting their own deluded presuppositions into the text, and are grossly redefining the meaning of a salvific doctrine [God’s grace]. Study church history to see what kind of men are notable for redefining soteriological terms. They are called heretics.