I myself have argued against Paul being the author of Hebrews on the basis of the contrasting style and absence of his otherwise uniform statement of his authorship, yet 2 Peter 3:15 seems to refer to this epistle, and thus I postulate that it may have been originally a synagogue address (to Christians meeting therein) that was penned by someone else, as with the gospels and the teachings of Christ.
But if you want to contend against the Pauline authorship of Hebrews than that is fine with me. However, then you need to thus attribute error to your own council of Trent:
the books that are received by this Synod. They are as set down here below...fourteen epistles of Paul the apostle, (one) to the Romans, two to the Corinthians, (one) to the Galatians, to the Ephesians, to the Philippians, to the Colossians, two to the Thessalonians, two to Timothy, (one) to Titus, to Philemon, to the Hebrews (The Council of Trent - Session 4; http://www.thecounciloftrent.com/ch4.htm)