Some thoughts…
i) The Epistle to the Hebrews is addressed primarily to Hebrew-Christians who were sorely tempted by various pressures to abandon Christianity and back slide into Judaism.
ii) Hebrews 6 is specifically about Jewish Christians who abandon Christianity.
iii) For a moment I will remove some of the statements St.Paul makes between Hebrews 6:4-6:6 so as to make his point clearer. I’m not saying the other information isn’t important - however, it is only illustrative of his main point.
“For it is impossible for those who were once enlightened …, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame.” (Hebrews 6:4a, 6b)
Calvinist readings of this passage seem to leave out the “seeing they crucify to themselves the Son of God afresh, and put him to an open shame” part. It is that part which provides the essential context to the passage. St.Paul is speaking not simply of those who fall away from the Church, but very specifically of Jewish Christians who apostacize and return to Judaism. The nature of their betrayal is much more profound as it is not simply unbelief but a very clear indictment of Christ and the same form of unbelief which those who put Christ to death suffered from.
Also, the word translated “impossible” here, in the Greek, is not as emphatic as the English word perhaps is. Adunatos literally means “without strength” or “without power” - the same word is used in Acts 14:8 to speak of a crippled man’s feet (“impotent”). So while it could be taken to be an “absolute impossibility”, I think the context (specifically St.Paul’s perceived need here to illustrate his point) shows that this wasn’t an attempt at taking a doctrinal stand about the utter impossibility of a defecting Jew returning to the Church, but simply a statement of how incredibly far a fall and how deep a betrayal such an apostasy would be.
And you see, that’s the thing - this passage is very clearly about life in the Church. It mentions illumination/Baptism, heavenly gift/Holy Communion, and participation in the Holy Spirit/Chrismation. How could someone after all of this (especially keeping in mind the rigorous preperation which was normal for receiving these sacraments of initiation in the early Church, which were typically all administered at once hence why St.Paul speaks of them as he does), who turns around and defects back to Judaism, be reasonably expected to return? It’s a very sad situation. But in context (especially the broader context of the New Testament on this topic) it doesn’t add up to what our Calvinist friends are choosing to believe. Indeed, their interpretation is untenable since it involves cases where only sophistry on their part could justify the situation. Ex. say one of their members defects, but then changes their mind and comes back to the congregation and the practice of their Reformed/Baptist/whatever religion. Well if they’re following St.Paul at all literally here, they’d have to refuse to take someone like that back. Yet they likely wouldn’t - instead, they’d say “oh, they didn’t really fall away”. Of course, that’s exegetically nightmarish - they go from being overly literal to being rather loose and creative with context all at once, seemingly wherever it suits their peculiar teachings.
