After an elaborate exordium (1.1-4) and the extensive catena of OT quotation (1.5-13), Auctor shifts his genre from exposition to exhortation in 2.1-4. While it may be easy to logically pick up on the surface the connection between ch.1 and 2.1-4, there are some important factors that aide in connecting the two different genres and moving the argument forward in a cohesive manner.
First, it is important to note the many semantic similarities that are shared between the two units of discourse. For example, we are told at the onset that God spoke through the prophets (Πολυμερῶς καὶ πολυτρόπως πάλαι ὁ θεὸς λαλήσας τοῖς πατράσιν ἐν τοῖς προφήταις) as well as through a son (ἐλάλησεν…ἐν υἱῷ). Also, the catena of OT quotes consists of God speaking either about the angels or the son (1.5-13). The whole of the chapter focus on some aspect of God speaking. This focus on speech continues into ch.2. Note the warning to pay close attention to what was heard (Διὰ τοῦτο δεῖ περισσοτέρως προσέχειν ἡμᾶς τοῖς ἀκουσθεῖσιν), the mediatorial work of the angels at Sinai (εἰ γὰρ ὁ διʼ ἀγγέλων λαληθεὶς λόγος), the word spoken by the Lord and confirmed by those who heard it from the Lord directly (ἥτις ἀρχὴν λαβοῦσα λαλεῖσθαι διὰ τοῦ κυρίου ὑπὸ τῶν ἀκουσάντων εἰς ἡμᾶς ἐβεβαιώθη). All of these references to speech/hearing form a semantic chain which provides 1.1-2.4 with a cohesive tie.
Also, the Διὰ τοῦτο serves as a marker indicating a conclusion to ch.1. The warning which Auctor is driving home is contained in the conditional clause in 2.2-3:
εἰ γὰρ ὁ διʼ ἀγγέλων λαληθεὶς λόγος ἐγένετο βέβαιος καὶ πᾶσα παράβασις καὶ παρακοὴ ἔλαβεν ἔνδικον μισθαποδοσίαν, πῶς ἡμεῖς ἐκφευξόμεθα τηλικαύτης ἀμελήσαντες σωτηρίας, ἥτις ἀρχὴν λαβοῦσα λαλεῖσθαι διὰ τοῦ κυρίου ὑπὸ τῶν ἀκουσάντων εἰς ἡμᾶς ἐβεβαιώθη
For if the message spoken through angels was valid, and every transgression and disobedience [refusal to listen] received its just payment, how shall we escape if we disregard such a magnificent salvation? This message of salvation was first declared by the Lord and then confirmed to us by those who heard
The comparison in ch.1 between the angels and Christ is a comparison between messengers. Christ, because he is son (1.2, 5) is a far greater messenger than the angels. Therefore, the message which God has proclaimed through Christ (ἐπʼ ἐσχάτου τῶν ἡμερῶν τούτων ἐλάλησεν ἡμῖν ἐν υἱῷ) is greater than the mediatorial work of the angels, who served likewise as messengers of God at Sinai.
More can be said, but it is getting late. In closing, Auctor will later refer to Christ as the Apostle of our confession (3.1). Instead of thinking of apostle in terms of an appointed position (i.e. the Twelve Apostles), think of it in its functional sense, what an apostle does. Apostle, angel, and prophet are all messengers who are sent to proclaim a message; this is the focus of Heb 1-2. Christ is God’s final communicative agent.
I am grateful for the work of Cynthia Long-Westfall who has informed much of my thinking on this section. It is nice to be able to have an insight on something and then to have it confirmed by an expert in the field.