The NT doesn't really make the OT obsolete. The NT is not a complete doctrine by itself. Paul and other early church leaders did the best they could to tie the two together, but the Paul was not a top notch Rabbi, if he was a Rabbi at all. He really didn't understand the logical system that was the beginnings of the modern rabbinical system the Jews have today.
Explaining the relationship between the OT and the NT is a big part of what Christian religious leader do and how they maintain they status as religious leaders. Showing the lack of a strong logical thread between the two books is just going to be considered proof that you don't get it.