Good description of "dogs" in Phil 3 by Stephen Bradd:
Paul first declares - "Beware of dogs". Obviously, he's not warning them about any literal four-legged dogs, but he is warning them about humans who were behaving like dogs. From the other warnings in this immediate context, we know that Paul was referring to the Judaizers (i.e., certain Jews who had been baptized and who were determined to force Gentile Christians to keep the law of Moses, particularly regarding circumcision). They were like dogs in that they were constantly barking out their false doctrine, hounding Paul, and biting and devouring others with their error.