3:1
While the NIV says “Further, my brothers” the ESV says “Finally, my brothers”, the Greek actually says “The rest ...”. Some of thought that this signifies the end of a letter and have sought to argue that what we have is actually composed of two letters. However, there is no need for this conjecture. Paul often went into digressions, just as a preacher saying “finally” is no promise at all that the end is near! He is about to warn them about the false teaching of the need for circumcision, and with it the need to obey the Law. This is a subject which arose almost wherever Paul went, Galatia is the most prominent example, and it was the major topic at the Council of Jerusalem (Acts 15). “To write the same things again” seems a little out of place, but we should remember that Paul had been with the Philippians on two occasions (assuming he is writing from Rome), and he would almost certainly have spoken to them about these matters. So he is about to warn them again. He is doing this to safeguard them, to protect them. Part of our duty as teachers and preachers is to protect people from false teachings.
3:2
Paul refers to the false teachers, the Judaizers, in no uncertain terms. “Those dogs”. Now “dogs” was a term that Jews used of Gentiles, so Paul is full of contempt for the Judaizers. He describes them as evildoers and mutilators of the flesh. This latter phrase is a derogatory way of referring to circumcision. Note that Paul does not seek “to understand” the point of view of the Judaizers! There is a time when we should not be nice about our opponents or about false teachers. False teaching is dangerous, it leads people astray and can lead them to hell. At present there are those in the church who seek to change the Bible’s teaching on sexual morality. We should not engage in “constructive” dialogue with such people for they are deceived and are seeking to deceive.