Hebrews does not contain Paul's standard greeting; Paul learned directly from Christ and the author of Hebrews learned from previous followers of Christ; Paul agreed with James, John and Cephas [Peter] that he would go to the Gentiles and they would go to the circumcision [Hebrews], as seen in Galatians 2.
It is sheer speculation as to who wrote Hebrews. There is still a possibility that he did. The tradition of Pauline authorship is old and has not been decisively disproved. Origen is right that only God knows who wrote the book.
The style is not typical Pauline, but this is a subjective argument. It is not inconsistent with Pauline thought. Other possibilities are Barnabas, but this cannot be proved anymore than Paul can be disproved. Other more unlikely suggestions are Clement, Luke, Silvanus, Philip, Priscilla, Apollos. The bottom line is that it is inspired, canonical.
Paul was not in the good book of Jews. Given the purpose and target audience, Paul did not have to use his standard greeting.
Paul did learn directly from Christ, but he also learned from the disciples/apostles who walked with Jesus about the historical Jesus. He spent time hearing their stories and understanding historical details that were not directly revealed like the gospel, etc. (both/and, not either/or).
Paul reached Jews and Gentiles, but became the main one to expand the one gospel to the Gentiles. The others also reached Gentiles, but started out and continued a ministry to Jews.
Paul's background and credibility suit him to contextualize the revealed gospel to a Jewish or Gentile audience. Gal. 2:7 is a demarcation of ministry, NOT a proof text for two true gospels (consider Gk. use of Genitive here not brought out in KJV).
MAD is basically begging the question and reading a preconceived view into a few texts out of context. It does not exegete other texts properly or build a case on all relevant verses.
I realize this will get me a neg rep from Nick, a blah blah from LH, but I hope it helps some others.
So, Barnabas is a good possibility, but we cannot rule out Paul. MAD or non-MAD should not rise or fall on the authorship of the book, but the contents of the NT.
Romans and Hebrews are both great statements of the gospel with one being contextualized to a Jewish audience (OT references, etc.), while the other also had a Gentile bent (Rom. 1, etc.). Either way, Jew/Gentile are one in Christ/Body of Christ post-cross, not post-Paul.
