For many, this is a pretty boring chapter at the end of a highly contentious and therefore interesting epistle. It is argubly the most important epistle of the whole of the New Testament as it includes both doctrine and advice.
Many, Christians and others, probably treat it like one of the genealogies and lists of tribal histories - perhaps even skipping over it in their efforts to get to the exciting stuff.
However, if one looks at it carefully, it is full of a lot of exciting things.
Of the 27 people Paul mentions, at least 9 of them are women. What is more, the first two to be mentioned are women. Phoebe is described as a 'servant (deacon - NIV) of the church at Cenchrea' - where the word 'servant' is used to translate the Greek word "διάκονον" (diakonon). This word is the same root word used twice in Acts 6: 1-7, when the apostles chose the 7 to serve - thus instituting the office of practical leadrship that was the diaconate in the early church: "προσκαλεσάμενοι δὲ οἱ δώδεκα τὸ πλῆθος τῶν μαθητῶν εἶπαν· Οὐκ ἀρεστόν ἐστιν ἡμᾶς καταλείψαντας τὸν λόγον τοῦ θεοῦ διακονεῖν τραπέζαις·" (v.2) and "ἡμεῖς δὲ τῇ προσευχῇ καὶ τῇ διακονίᾳ τοῦ λόγου προσκαρτερήσομεν." Clearly, she plays an important role in the church that is mentioned; she's not just a member of the congregation.
Interestingly, the next person mentioned is "Πρίσκαν" - Priscilla (along with her husband Aquila), v.3ff - and their role as leaders of the church that met in their home. Again, someone in a not-insignificant role.
The third woman to be mentioned is "Μαριάμ" - Mary - v6. Apart from her name and the fact that she had worked hard for the church (and was now in some form of 'retirement' from this role), we don't know anything about her.
Verse 7 includes the name "Ἰουνίαν" Junias/Junia. In view of the fact that all the women whose Greek names end in 'a' (a common ending to feminine nouns) end in ' ...-αν' in this passage ( because they are always the objects of the sentence, not the subject) it would make sense to understand this to be a female name associated with a husband - Andronicus. They had both been in prison with Paul, suggesting that they both held leadership roles of some kind - perhaps, like Paul, in a missionary capacity.
In v.12, Paul mentions three women - Tryphaena, Tryphosa and Persis; and then Julia and the sister of Nereus in verse 15. Of the nine, six are described as fellow-workers or as those who have worked very hard in the Lord (v12)
Clearly, the early church was not an organisation which ignored women in its leadership.
I accept that since the middle of the 1st millennium - especially following the Synod of Whitby (664) - the church has been predominantly male-run, but tht isn't a Biblical position.