Why do Jews find the term Old Testament offensive?

A Jewish person would consider it offensive because it could insinuate that that the Torah is no longer valid, having been replaced by something new (New Testament).

Usually, Jews do not find the term Old Testament offensive, just inapt. The Old Testament is different from the Jewish Bible or Tanakh in that it has additional books, a different order to the books, different translations of key Words (usually in support of Christology) and additional material in certain books. As a result, the Jews prefer to say that they read the Tanakh than that they read the Old Testament.