Author of Hebrews
It is generally assumed that Paul is the author of Hebrews because he wrote most of the other epistles that was included in the Bible. However, Hebrews is not signed with a signature like all the other epistles which is the reason why scholars debate on whom the author is.
"The Epistle to the Hebrews is anonymous, and it is not known who the author is." -- John Calvin ("Calvin's Commentary on Hebrews", translated by John Owen)
The book of Hebrews is not signed
Could Paul have written Hebrews and just intentionally left off his name so that the Jews would be more accepting of the epistle? This scenario is impossible for two reasons.
Paul concluded 2 Thessalonians 3:17: *“The salutation of Paul with mine own hand, which is the token in every epistle: so I write.” And he closed Colossians 4:18 with: “The salutation by the hand of me Paul. Remember my bonds. Grace be with you. Amen.”* Paul never wrote anything without signing his name to it, either before or after. Romans, the two Corinthian epistles, Galatians, Ephesians, Philippians, Colossians, the two Thessalonian epistles, the two epistles to Timothy, the epistle to Titus, and the epistle to Philemon — all of these epistles begin with the name, “Paul.” Unlike the books of Romans through Philemon, the book of Hebrews neither begins nor ends with Paul’s name...
Regardless of who wrote it or spoke it, an unbelieving Jew wanted nothing to do with God’s Word. The unbelieving nation of Israel refused to hear from Apostles James, Peter, John, et cetera, in early Acts. Apostate Israel did not like Jesus Christ, either in His earthly ministry or in His apostles’ ministries in early Acts. Unbelieving Israel considered Jesus a fraud. Period. Just look at how violently Israel’s leadership reacted when Stephen rebuked them for killing Jesus (Acts 7). After his great sermon documenting their history of unbelief, the Jews mercilessly stoned their fellow Jew, Stephen, to death! Paul leaving his name off Hebrews because the Jews would reject it, is not persuasive. Its writer aside, the contents alone of the book of Hebrews is unpleasant to someone who refuses to accept Jesus as Messiah. The book of Hebrews emphasizes that Jesus Christ is God’s Son, the fulfillment of the Old Testament economy. If the omission of Paul’s name from Hebrews was done in an effort to make the epistle more acceptable to Jews, should not God have also avoided mentioning Jesus as Christ in the epistle, too? Again, anyone who wrote Hebrews was offensive to apostate Israel because Hebrews itself contains offensive doctrine about Jesus Christ.
Contradicts Paul
The writer of Hebrews received second-hand information from the apostles: *“How shall we escape, if we neglect so great salvation; which at the first began to be spoken by the Lord, and was confirmed unto us by them that heard him;” Paul never received second-hand information from the 12. According to Galatians 1:11-12, the Lord Jesus taught Paul directly: “But I certify you, brethren, that the gospel which was preached of me is not after man. For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.” Notice what Paul wrote when he discussed how he met with Israel’s apostles in Jerusalem: “But of these who seemed to be somewhat, (whatsoever they were it maketh no matter to me: God accepteth no man’s person:) for they who seemed to be somewhat in conference added nothing to me”* (Galatians 2:6). The 12 apostles did not teach Paul anything. In fact, if you further study Galatians chapter 2, you will learn that Paul taught them something. He taught them the further revelation and advancement of God’s purpose and plan. You can also see Acts chapter 15.
Not one of the original 12 apostles
Hebrews 2:3-5 helps us one more to rule out individuals who did not write Hebrews: *“How shall we escape, if we neglect so great salvation; which at the first began to be spoken by the Lord, and was confirmed unto us by them that heard him; God also bearing them witness, both with signs and wonders, and with divers miracles, and gifts of the Holy Ghost, according to his own will?”*
Notice how the writer of Hebrews refers to people who heard Jesus in His earthly ministry as “them that heard him.” The writer of Hebrews says that what “they” heard “we” heard from them. In other words, the writer of Hebrews is someone who was not present in Matthew through John. Someone present during Christ’s earthly ministry taught doctrine to the writer of the book of Hebrews. Concerning the penning of the book of Hebrews, we can rule out Peter, James, John, et cetera. All of Israel’s 12 apostles can be eliminated as possible writers of Hebrews. The 12 continued throughout Jesus’ earthly ministry. They would not need to hear that information secondhand because they had heard Him firsthand. They had witnessed all those miracles firsthand.