Acts 16:1-3 reads:
1 Paul went on also to Derby and to Lystra, where there was a disciple named Timothy, the son of a Jewish woman who was a believer; but his father was a Greek. 2 He was well spoken of by the believers in Lystra and Iconium. 3 Paul wanted Timothy to accompany him; and he took him and had him circumcised because of the Jews who were in those places, for they all knew that his father was a Greek.After deciding to recruit Timothy to his mission team, Paul had three options
3 τοῦτον ἠθέλησεν ὁ Παῦλος σὺν αὐτῷ ἐξελθεῖν, καὶ λαβὼν περιέτεμεν αὐτὸν διὰ τοὺςἸουδαίους τοὺς ὄντας ἐν τοῖς τόποις ἐκείνοις, ᾔδεισαν γὰρ ἅπαντες ὅτι Ελλην ὁ πατὴρ αὐτοῦ ὑπῆρχεν.
1. Leave Timothy uncircumcised and present him as uncircumcised in the mission field.
2. Leave Timothy uncircumcised and let others assume that he was circumcised. This was a real option (see b. Yev 45a-b and see here).
3. Circumcised Timothy.
At first sight it seems odd (to us) that Paul should circumcise Timothy soon after winning an agreement that circumcision is not necessary (Acts 15). We can assume that Acts 16:3 explains this apparent contradiction, at least to the satisfaction of the intended audience.
In Acts 16:3 Luke gives two reasons why Paul chose option 3.
(i) He wanted Timothy to accompany him.
(ii) The Jews in those places all knew that Timothy's father was a Greek.
Luke accompanied Paul and Timothy on the second missionary journey. Most commentators assume that Luke was a Gentile (and that Titus remained uncircumcised). If this were the case, then being a circumcised Jew was not a necessary qualification for being an effective missionary partner on the second missionary journey. So, if Luke was a Gentile (and was presented as such), then reason (i) was insufficient to rule out option 1. On the assumption that Luke was a Gentile, most commentators then conclude that Acts must be saying that option 1 is ruled out by a combination of reasons (i) and (ii), and that option 2 is not considered. They suppose that the Jews tolerated Luke, an uncircumcised Gentile, but would not have tolerated an uncircumcised son of a Jewish woman. This is problematic, not least because the text does not say "they all knew that his mother was a Jew". It says that they all knew that his father was a Greek. Furthermore it is not clear that an uncircumcised son of a Jewish women would have been any more objectionable to anyone than an uncircumcised son of two Gentile parents, since matrilineal descent did not pertain in the first century.
If, on the other hand, Luke was a Jew (see my recent posts), then all of Paul's missionary partners were circumcised (Barnabas, Mark, Silas, Timothy, and Luke). This then raises the possibility that Luke expected his audience to know that Paul's missionary partners had to be circumcised (to be able to have effective ministries in synagogues). We can assume that the audience of Acts knew much more than we do about the required qualification of Christian missionaries in their day. This allows a very different understanding of how Acts 16:3 explains why Paul circumcised Timothy: Luke wrote reason a) to explain why Paul did not choose option 1, and he wrote b) to explain why Paul did not choose option 2. That is to say, Luke wrote "Paul wanted Timothy to accompany him" and the readers knew at that point that it would be necessary for Timothy to at least pass as a Jew. He then wrote "for they all knew that his father was a Greek", which implies that they all knew that Timothy was uncircumcised. Luke wrote this to show that Paul would have let uncircumcised Timothy pass as circumcised (option 2) if people had not already known that he was uncircumcised. Thus Luke communicates that the circumcision of Timothy was not ideological but was merely expedient.
To sum up, in Paul's lifetime his missionary partners would not have been effective in their work if others knew that they were uncircumcised (whatever their parentage). Timothy could not pass himself off as a circumcised Jew because the Jews already knew that his father was a Greek and that therefore he was uncircumcised.
For me, this understanding of Acts 16:3 is confirmed by Gal 2:3-5
But not even Titus, who with me was a Greek, was compelled to be circumcised. But because of false believers secretly brought in, who slipped in to spy on the freedom we have in Christ Jesus, so that they might enslave us - we did not submit to them even for a moment so that the truth of the gospel might always remain with you.I infer from this that the circumcision of Titus (who was also called Timothy) had been misunderstood. The Galatians thought it indicated that Paul had yielded to the position of the agitators, but Paul points out that it was only because the agitators had, by spying, found out that Titus-Timothy's father was a Greek. For more on Titus-Timothy, see here.