It seems to me that in order to understand the New Testament you need to Read the Old Testament...so why do some Protestants not read it?
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Well, the reasoning is two-fold.
First, most people don't read the Old Testament because most protestant preachers rarely teach from the Old Testament. Because of that, they don't see the need to go over it. (Sad, but I've heard this argument before.)
Secondly, there's the concept that Jesus fulfilled the law and we, therefore, are no longer under the law. This comes from (among other places) here:
Now, since we are no longer the old law, most people find it difficult to directly apply to our lives. If you compare this to the New Testament (particularly the epistles), the utility seems to be dramatically greater in the New Testament.
A correlation to the second part is that anything that we should follow is in the New Testament. The idea is that if it was repeated by the apostles or Jesus, then it is worthy of study; otherwise, it's just extra words to try to absorb that no longer apply.
An example of this:
Acts 15:28-29 (NIV) 28 It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: 29 You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things.
Here, Paul repeats some commands from the OT. Since they're in the NT, they should be learned. Anything that's not in the NT, can safely be ignored.
OK, don't stone me. I'm not saying this is a valid justification. It's just what I've learned about "some Protestants".
I am a Protestant, and I love the Old Testament. The Old Testament prophets laid the foundation of our faith!