Chapter 2 ends with Paul's famous quotation on Christ living through him:

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           I have been crucified with Christ and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave himself for me. I do not set aside the grace of God, for if righteousness could be gained through the law, Christ died for nothing! (Gal 2:20-1)

         

The "I" that was crucified was the old man, whether Gentile sinner or Law-abiding Jew.  The man who is raised up in place of the old man is singular, "one new man," the life of Christ abiding in both Jew and Gentile.  We are to live not according to the old rights and wrongs (sins and laws), but according to the new Spirit and faith.  This is the only moral way to live, ie. "righteous", acceptable to God.  We cannot graft the new way of life onto the old one.  Not only has the old man died, but the old Law has too, because this Law forced a division between Jews and Gentiles that can no longer be maintained in the body of Christ.  To attempt to retain these distinctions is to "set aside the grace of God."