Connecting Old and New Testament dogs

In Philippians 3:2, Paul referred to some of his opponents as "dogs", specifically Jewish Judaizers. As said in class, this was typically a name that was given to the Gentiles by the Jews, so Paul calling other Jews a dog had to have hacked some folks off. The J.J.s could have picked up on Proverbs 26:11 from having studied the OT to great lengths. This verse says that dogs return to their vomit, just as fools return to their foolishness. Although the J.J.s were covered by grace, they reverted back to their old ways of strictly following the law in an attempt to obtain salvation. Peter also addresses the issue in 2 Peter chapter 2. He tears into false teachers who have the knowledge of Christ and have experienced salvation through grace, but deceive others by teaching that they have to observe the old law that was fulfilled through Christ. Simeon Peter references Proverbs 26:11 in in saying that they, like dogs, have returned to their own vomit, that "it would have been better for them to have never known the way of righteousness than, after knowing it, to turn back from the holy commandment delivered to them (2 Peter 2:21-22). Apparently the problem with this heresy persisted even after Paul addressed it in Philippians, and Simeon Peter and possibly even Paul utilized OT Scripture that would have rang a bell with the Jewish Judaizers and called them out for the foolishness that they were teaching, and causing others to be led astray.