So why Greek? Specifically Koine. Koine was the common dialect of Greek back in the first century AD. It was the language that was understood by the common people. So this was the language that the New Testament was written in.
For me, at least, the desire to learn Greek stems from a desire to understand the Bible better. That and there is just something mysterious and cool about the language to me.
Languages fascinate me. If I had the time, energy, and dedication I would want to learn Greek, Hebrew, Latin, and Russian. I think those languages are so important in the Biblical world and in the development of our culture.
Anyway, I'm getting off-topic perhaps. Understanding Greek gives us a better knowledge of the Scriptures and draws us closer to God and His Message of why He sent His Son to Earth. In the Greek we are able to pick up on some of the nuances of the NT and gain a deeper understanding of the Scriptures.