Hi Bible man,
As I was reading through the commentaries to see what they had to say, this from Gill gave very strong reasoning as to why it's author was Paul. Here is the main points he makes.
John Gill's Exposition of the Entire Bible--
That this epistle was written very early appears from hence, that it was imitated by Clement of Rome, in his epistle to the Corinthians, who took whole sentences out of it; and therefore it could not be a new work, as Eusebius (a) observes:
It has been ascribed to different persons, as to Barnabas, to Apollos, to Luke the Evangelist, and to Clement of Rome, but without any just reason. Clement of Alexandria, a very ancient writer, asserts it to be the Apostle Paul's (d); and his name stands in the title of it, in all R. Stephens's exemplars, and in all Beza's copies, excepting one, and so it does in the Vulgate Latin and Arabic versions;
from the order and method of it, first treating of doctrines, and then proceeding to practical exhortations, which is the common form of Paul's epistles: to which may be added various circumstances; as that it was written from Italy, where Paul was a prisoner; and the mention the author of it makes of his bonds, and of Timothy, as well known unto him, who was Paul's companion; besides, the token of his epistles appears in this, namely, his usual salutation to the churches; see Heb_13:23. But above all, the testimony of the Apostle Peter is greatly in favour of its being his, 2Pe_3:15 from whence it clearly appears, that the Apostle Paul did write an epistle to the Hebrews; for to them Peter wrote; see 1Pe_1:1 and what epistle could it be but this? and what Peter refers to is to be found in it; see Heb_10:25
The common objections to its being his are, its not bearing his name, the diversity of its style, and the author of it seeming to be not an apostle, but a disciple of the apostle's: as to his not setting his name to it, the reasons might be, because he was the apostle of the Gentiles, and not so much of the Jews; and because of the prejudice of the Jews against him, both believers, and unbelievers; wherefore had his name been to it, it might have prevented the usefulness of it to the one, and have stirred up the rage of the other: as to the difference of style, different subjects require a different style; and yet in many things there is a likeness, as before observed: and as to the author's not being an apostle, which is concluded from Heb_2:3 the word "us" there is to be understood of the believing Hebrews, the disciples of the apostle, and not inclusive of the author, by a figurative way of speaking often used by Paul; and besides, the apostle received a confirmation of the Gospel from Ananias, who might have been an hearer of Christ, though he was at first taught it by Christ himself; add to this, that whoever was the writer of it, it was written before the destruction of Jerusalem, and when several of the apostles were living, and therefore he could never design by those words to put himself in a succeeding generation. Dr. Lightfoot places it in the year 62, and in the eighth of Nero.
Hope this is helpful.
mercy, peace and love
Kat