Chr*stianity did not claim to "extend the faith to all peoples." It claimed to replace `Am Yisra'el with the chr*stian church and the Torah with a post-Biblical ceremonial drawn mostly from paganism.
.....here we go again, that is soooo Fourth Century. The history of Judaism is a string of Covenants between the Jews and God that were broken by the Jews. Jesus came to bring a new and everlasting covenant, replacing all that came before it. This new and everlasting covenant is not exclusive to the "chosen" people, but available to all who will believe and follow the word of God.