Your question is not a silly question at all! So, how come we are not Jewish?
Not surprisingly, actually, your question is raised in the book of Acts, chap. 15. There are some guys who were saying to non-Jewish believers: ‘You need to be a Jew in order to be saved.’ Peter says (my paraphrase), ‘God doesn’t distinguish betweeen Jew and Gentile, but he saves both by faith. So, you don’t have to follow the Old Testament Jewish Laws like circumcision because these are like a yoke that neither we nor our forefathers were able to carry but believe that is through the grace of Jesus that we are saved’. What Peter is saying is that the Jews were unable to follow the Law of the Old Testament and God promised a better way of relating to him (see Ezek. 36:33-38). The difference is that the promises were not for just the Jews but all humanity.
Jesus came into the world in order to fulfill all these promises (2Cor 1:20) - that is why Jesus had to be a Jew. In short Jesus didn’t come to establish Judaism for all to follow, he came as the Christ (that is the long expected and anticipated King from the Old Testament) to establish CHRISTianity not as a set of laws to follow but as a life of following the CHRIST.
In the Old Testament the Jews (Israel) were chosen to be God’s special people through whom God would be seen for who he was and be glorified. Israel was the nation that the world came to to find God. In the New Testament this “nation” is no longer Israel but has expanded to become all who follow Christ. And we now go to the nations (Matt 28:19) to tell them, not to become Jews, but to follow Jesus as the Christ.
From my limited understanding this is what Jews for Jesus are doing. They believe that Jesus is the long awaited Christ and they are out there telling as many Jews as they can. Good on ‘em I say.
So, let’s get on with following Jesus and his heart of obedience.
Hope that goes some way to answering your question.