Reading Philippians after Supersessionism

Paul's letter to the Philippians has often been read as one of the apostle's clearest denials of his (previous) Jewish identity in order to preempt the "Judaizing" tactics of false teachers who might infiltrate the congregation. But is this really the problem that Paul is confronting? And did Paul really abandon his identity as a Jew in order to "know Christ"? Furthermore, what should Paul's gospe...