One of the classic cases of modern religious sensitivity today is the question of what to call the two sections of the Christian Bible. Calling the first section the "Old Testament" does not seem as appropriate these days, now that Christians are doing a much better job at respecting their Jewish neighbors. Sensitivity to our Jewish neighbors is only one reason, however, to change the name for the so-called Old Testament. Recently, in my encounters with several people (students and otherwise), I found several other reasons that made me think using the label "Old Testament" was actually working against Church teaching about scripture.
Firstly, because the first section of the Bible is labeled "Old", many people take the attitude that it is no longer relevant, and, therefore, they do not need to study this portion of scripture. This, of course, is erroneous. After all--if you're arguing that Jesus "fulfills" the promises made in the Hebrew scriptures, you can't very well act as if they are no longer relevant. If they are irrelevant, than Jesus is irrelevant.
Secondly, people tend to over simplify the very complex theology found in the Hebrew Scriptures. They will talk about the "God of the Old Testament", as if that God was not the very same God that Jesus called Father. This is a grave error, as well, since the Church does not teach that the God of the Hebrew Scriptures is not the same God as the God of the Christian Scriptures. They are the same God. If there appear to be contradictions or development in thought, then those things have to be addressed, not dismissed by labelling one "old" and one "new".
[An aside: The truth is, as I see it, there are multiple presentations of God in the Hebrew Scriptures, based on the personality type of the human author telling us the story. There's the wrathful/all powerful, warrior God; the God who comes down to earth and eats and talks with people; the Good Shepherd; the Holy Spirit; Lady Wisdom; the God who demands sacrifise; the God who rejects sacrifise in favor of charity; the patient God; the impatient God; the God who rejects sinners; the God who loves sinners. It's the God who chose beloved Israel from among all the nations and tribes of the world--but who chose Israel for the sake of all the other nations and tribes. Yes--a God for the person, and a God for the world. In truth, the Hebrew Scriptures won't allow us to put God in a little definitional box. They say to us--there's more to God than our experiences of him.]
Thirdly, Christians get the impression that because they have a "New Testament" that somehow the other one is null and void. This is erroneous, too. God's covenant with the Jewish people remains in effect. "Old" is problematic here, only because it is used to sometimes means "a covenant that used to be", and not "the first or ancient covenant".
Where does the Church spell some of what I have said out?
1) The Dogmatic Constitution of the Church (Lumen Gentium) [especially ch. 2]
2) The Declaration on the Relation of the Church to Non-Christian Religions (Nostra Aetate)
3) The Dogmatic Constitution on Divine Revelation (Dei Verbum)
Of course, "Old Testament" is a perfectly good name for the first section of the Bible, since it does recognize the fact that there was a previous covenant made by God with humanity before the "New Testament" given through the Incarnate Word, and it was through this "old" covenant that God prepared the world for the "new". "Old", then, in this sense, is a mark of honor, as it speaks to the ancient and revered character of this previous covenant. If only people would use the phrase in that way.
My motivation in saying all this is to spread the word that the Catholic Church honors and respects the Hebrew Scriptures as truly the revelation of God, to be studied by all the faithful as a means of understanding and loving God, his son, Jesus Christ, and the Holy Spirit, author of both the Hebrew and Christian scriptures. The Bible is one book made up of many stories and voices. It's only one book, and all the parts go together to give us the message about who God was for our ancestors in faith, who he is for us today, and who he will be for those to come. It is our life's work to study the text, and so live and believe what we have been taught.