John Owen advocated a theological argument for limited atonement. A biblical or exegetical argument would be 1 John 2:2 and 5:19. Charles Ryrie discusses this biblical or exegetical argument: The only other occurrence of the phrase “the whole world” in John’s writings is in 1 John 5:19, and there it undebatably includes everybody. So, the presumption is that it also means everyone in 2:2. And this means that Christ died for all people even though all are not ultimately saved.[1] In other words, the extent of Satan’s influence in 5:19 is unlimited, and so is the extent of Christ’s atonement in 2:2 unlimited
John Owens theological argument is called the Double Payment Argument, which argues if Christ paid for the sins of all sinners and all the sinners who do get saved pay for their sins in hell then there is a double payment for sins: “Is it probable that God calls any to a second payment, and requires satisfaction of them for whom, by his own acknowledgment, Christ hath made that which is full and sufficient?”[2]
Nowhere in Scripture is it taught that sinners in hell are paying for their sins. They are in hell for rejecting Christ as their saviour. For sure, they are experiencing God’s wrath or punishment: “These will go away into eternal punishment, but the righteous into eternal life” (Matthew 25:46). But, nowhere in God’s Word is it taught that sinners are paying for their sins in hell for eternity. To the contrary, Paul declared that “Christ Jesus, who gave himself a ransom [ransom is one of the words for redemption in the NT] for all” (1 Tim 2:6). Paul had been using the word ἄνθρωπος [anthropos from which we get our English word anthropology] for mankind without exception in 2:1-6. In 2:8, Paul will use the word ἀνήρ [aner] for the men who are distinguished from the women in the public worship service. Paul declares that Christ gave himself a ransom for all, that is, all, without exception. This same word for ransom [ἀντίλυτρον antilytron] in 1 Timothy 2:6 is used in 1 Peter 1:18-19, where Peter declares that we are not “redeemed [λυτρόω lytroo] with corruptible things .... but with the precious blood of Christ.” The provision of redemption was paid at the cross for all; it must, however, be appropriated by faith.
[1] Charles Ryrie, Basic Theology: A Popular Systematic Guide to Understanding Biblical Truth, Kindle Edition, 371.
[2] John Owen, The Death of Death in the Death of Christ (Edinburgh/Carlisle, Banner of Truth, 1967), 161.