The WTS explanation:
***w95 3/1 p. 19 "Old Testament" or "Hebrew Scriptures"—Which? ***
TODAY it is a common practice in Christendom to use the terms "Old Testament" and "New Testament" to describe the Hebrew/Aramaic and Greek language parts of the Bible. But is there any Biblical basis for using these terms? And for what reasons do Jehovah’s Witnesses generally avoid using them in their publications?
True, 2 Corinthians 3:14, according to the King James Version as well as some other older translations, such as the German Septembertestament, Martin Luther’s first translation (1522), may appear to support this practice. In the King James Version, this verse reads: "But their minds were blinded: for until this day remaineth the same veil untaken away in the reading of the old testament; which veil is done away in Christ."
However, is the apostle speaking here about the 39 books that are commonly called the "Old Testament"? The Greek word here translated "testament" is di·a·the´ke. The famous German theological encyclopedia Theologische Realenzyklopädie, commenting on 2 Corinthians 3:14, says that ‘the reading of the old di·a·the´ke’ in that verse is the same as ‘reading Moses’ in the following verse. Hence, it says, ‘the old di·a·the´ke’ stands for the Law of Moses, or at most, the Pentateuch. It certainly does not stand for the entire pre-Christian body of inspired Scripture.
The apostle is referring to only a part of the Hebrew Scriptures, the old Law covenant, which was recorded by Moses in the Pentateuch; he is not referring to the Hebrew and Aramaic Scriptures in their entirety. Furthermore, he does not mean that the inspired Christian writings of the first century C.E. constitute a "new testament," since this term occurs nowhere in the Bible.
It is also to be noted that the Greek word di·a·the´ke that Paul here used actually means "covenant." (For further information see New World Translation of the Holy Scriptures—With References, Appendix 7E, page 1585, published by the Watchtower Bible and Tract Society of New York, Inc., 1984.) Many modern translations therefore correctly read "old covenant" rather than "old testament."
In this connection, the "National Catholic Reporter" stated: "The term ‘Old Testament’ inevitably creates an atmosphere of inferiority and outdatedness." But the Bible is really one work, and no part is outdated, or "old." Its message is consistent from the first book in the Hebrew part to the last book in the Greek part. (Romans 15:4; 2 Timothy 3:16, 17) So we have valid reasons to avoid these terms that are based on incorrect assumptions, and we prefer to use the more correct terms "Hebrew Scriptures" and "Christian Greek Scriptures."