How did Richard Baxter support his arguments against John Owen (in 1649 and thereafter)?

In 1648 John Owen (1616-1683) published his definitive work The Death of Death in the Death of Christ which produced an almost immediate response, in the next year, from Richard Baxter (1615-1691) and an ongoing, controversial, public debate between the two. In a summary, in 1846, of Baxter's theology, Thomas W Jenkyn states part of Baxter's views as follows : >The atonement of Christ did not consist in his suffering the identical but the equivalent punishment (i.e., one which would have the same effect in moral government) as that deserved by mankind because of offended law. **Christ died for sins, not persons**. *The benefits of substitutionary atonement are accessible and available to all men for their salvation.* I have highlighted two parts with bold and italics. Paul specifically says that 'the Son of God loved me and gave himself for me', Galatians 2:20, and Peter says of Christ, that 'he bore our sins (not just 'sins' - 'our sins') in his own body on the tree', 1 Peter 2:24. This appears to be personal, to me. I cannot see how it could be more 'personal'. But I can see in Richard Baxter's theology the beginnings (or the first strong public expression) of what would later become a very widely accepted 'gospel' - that of a 'universally available' 'salvation' which, actually, applies to none, and has to be 'accessed' to 'activate' its efficacy. I am interested in how Richard Baxter supported his view, particularly regarding such texts as the ones I have quoted, where it would seem that scripture is not on his side in saying 'Christ died for sins, not persons' and 'the benefits are accessible and available to all' (when we are told that 'a sword turns every way to keep the way to the tree of life', Genesis 3:24.). This view is certainly the antithesis of what John Owen published and I am interested in what arguments Baxter relied upon to counteract Owen's theology. ------------------------- Personal Note : I have never agreed with the term 'limited atonement' since Jesus says, Matthew 20:28 and Mark 10:45, that the Son of man 'gave his life a ransom for many' (though 'strait is the gate that leads to life and and few find it' Matthew 7:14) and since John saw in vision, Revelation 7:9, 'a great multitude whom no man can number'. 'Many' and 'no man can number' does not sound 'limited' to my own ear. My own understanding is that some limit themselves, through unbelief, and exclude themselves from benefit and have only themselves to blame. That some are chosen 'before the foundation of the world', Ephesians 1:4, is irrelevant to the culpability of those who spend their life in activity contrary to their own humanity and detrimental to their own, ultimate, destiny. Perhaps Richard Baxter has arguments against what I have just written in which case I am interested in hearing about them.