Your reasoning above is as valid as the one below
A dog is a mammal
A cat is also a mammal.
Therefore a dog is a cat.
No one can dispute that the terms Jew and Gentile when used in a natural sense are always referring to ethnic race. For most of the old covenant period, circumcision meant being a Jew, being a Jew meant circumcision. Uncircumcision meant being a Gentile, being a Gentile meant circumcision. But this all changed under the new covenant. Physical circumcision lost its old covenant place of importance. It carries no spiritual benefit today because it has been superseded with spiritual circumcision of the heart. A true Jew today is not a man with the physical sign of the old covenant upon him but the spiritual sign of the new covenant – a circumcised heart.
The whole import of Paul’s teaching in Romans 2:17-29 revolves around defining what a real Jew is under the new covenant and what a true heathen is. Paul explains in Romans 2:25-29:
“if the uncircumcision keep the righteousness of the law, shall not his uncircumcision be counted for circumcision? ... For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit (
pneuma).”
Paul basically spiritualizes the terms circumcision and Jew to mean believer, and uncircumcision or Gentile to mean unbeliever. He teaches, if a man accepts Christ (regardless of his ethnicity) he is a spiritual Jew (or true circumcision); if a man rejects Christ (regardless of his ethnicity) he is a spiritual heathen (or true uncircumcision). Essentially, he is showing: Gentiles can become true Jews through faith in Jesus, and Jews can forfeit their right to be considered true Jews if they reject Jesus.
Paul further reinforces his argument in Philippians 3:3, speaking of the Church generally,
“For we are the circumcision, which worship God in the Spirit [Gr.
pneuma]
, and rejoice in Christ Jesus, and have no confidence in the flesh.”
This verse is another that presents a major difficulty for the literalists. Their insistence that every reference to Israel, Jew, children of Abraham and circumcision must be strictly interpreted literally is exposed by passages like this.
All through the New Testament the term “the circumcision” is used as a natural synonym for the Jews. Anywhere it is found, it is seen to describe (and encompass) the physical ethnic Jewish people. The term “the circumcision” in its normal usage related exclusively to natural Israel. We see this illustrated in Ephesians 2:11 where natural Jews are identified as “Circumcision in the flesh made by hands.”
Colossians 2:11-14 declares,
“ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead. And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross"
Several other references are found in Acts 10:45, 11:2, Romans 3:30 Romans 4:9, 12, 15:8, Galatians 2:7-12, Colossians 2:11, 4:11 and Titus 1:10. It must be added, the term did embody the stranger that joined themselves to Israel by faith in Yahweh. However, they too had to submit to all the customs pertaining to Israel in faith and practice, including physical circumcision.