Luther and Calvin noticed the same thing about 2:3, noting that Paul did not speak of his religious position in such a manner; he stressed his direct revelation from Christ (cf. Galatians 1:1-12). They also noticed the un-Pauline style and language, as well as affinities with Lukan style. Calvin supported the hypothesis originally advanced by Clement of Alexandria that the homily was written by Luke or Luke acting as Paul's interpreter, while Luther suspected that Apollos wrote it (particularly because of its use of typology which is distinctively Alexandrian; cf. its dependence on Wisdom) tho admitting that it is impossible to know either way.
Hebrews is, in fact, anonymous and makes no claims that it was written by Paul. This is probably the motivation behind the interpolation of mou "my" in 10:34 (= tois desmois mou from Philippians 1:16) in the Majority Text that was the basis of the Textus Receptus; hence the KJV refers to "compassion of me in my bonds". This pronoun is not found in the oldest MSS (e.g. P 13 P 46 A D H) and versions (e.g. the Syriac, Latin Vulgate, Coptic, Armenian), and thus does not appear in most modern critical editions and translations (cf. ASV: "them that were in bonds", NW: "those in prison").
The question is interesting however because the letter clearly has a Roman provenance or destination (cf. "those of Italy" in 13:24, which could either refer to those with the author in Rome or Italians accompanying the author elsewhere), it seems to be dependent on Romans (cf. 10:38 = Romans 1:17; 11:11-19 = Romans 4:17-21; 12:14 = Romans 14:19; 13:9 = Romans 14:3-5, 17; 13:20 = Romans 15:33), and Clement of Rome was the first writer to show dependence on Hebrews (cf. 1:3-13 = 1 Clement 36:2-5; 2:18-3:1 = 1 Clement 36:1; 3:5 = 1 Clement 17:5, 43:1; 3:7 = 1 Clement 13:1, 16:2; 4:12 = 1 Clement 21:9; 4:15 = 1 Clement 36:1; 6:18 = 27:2; ch. 11 = 1 Clement 9-12; 10:23, 11:11 = 1 Clement 27:1; 11:37 = 1 Clement 17:1; 12:1 = 1 Clement 19:2; 12:6 = 1 Clement 56:4; 12:9 = 64:1). The homily thus has an interesting connection with Rome and it was in existence by the late first century AD as the witness of 1 Clement shows; moreover, it itself is acquainted with the letters of Paul (cf. also parallels to 1 Corinthians and Galatians), so it may provide some data on the status and circulation of the Corpus Paulinum in the sub-apostolic period.