First of all, you will learn to think and to make thoughts in a different language, the original one.
You cannot imagine how it will change your mind and style of thinking. Our brain works in our language, thats how we think. If we learn a very different language, we learn how to think differently. For example you will get a new grasp of tenses and time which can change your acceptance of certain theologies, prophecies etc.
This applies to every foreign language you will learn, but, of course, many times more when learning the biblical language.
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Second:
The LXX. The LXX was used by the first Church and is quoted in the NT very frequently. If you do not use Greek, your Bible is a mixture of various incompatible sources.
Only reading all in Greek will give you a compatible OT and NT.
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Third:
Learning the original language will return to you other options of reading that are lost in a translation. When using translation, you read what the interpreter thought it means. All other meanings are lost to you, because you cannot reconstruct them from English.
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Fourth - in English, you loose the original emphasies. What is emphasised in Greek by the word order etc, is frequently lost in English translation, because English has a given word order and it cannot be changed.
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Fifth:
You will be more humble in teaching and understanding, because you will see how many possibilities of readings/understandings are actually in the original language, so you will not become a "one version bigot" saying all others are fanatics and idiots without faith, when they accept another possible meaning.
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Sixth:
It will help your theology and understading of first Christian literature, because you will not only know what the interpreter said to you it is, you will know what it is by yourself.
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To your question: Its quite hard to list some specific example of how this or that changed some meaning, I do not have any list of it... I only know that reading in Greek has given me new insight or better insight frequently. When I will get it again, I will write it down for these discussions