I live over the Green Line and I don't know how I feel about it

I'm sorry this post took so long. I'll admit, I have been dreading writing it since the moment I said I was going to in my last post, three weeks ago. I thought planning on writing a post would help me to make sense of my feelings about my exact location, but unfortunately it hasn't. Here goes nothing:
The Green Line is the colloquial term for the 1949 Armistice Line that was drawn up after Israel became a state in 1948. After the Six Day War in 1967 the Green Line was used as the line between Israel and the areas that were won in the war: West Bank, Gaza, Golan Heights, and Sinai Peninsula (returned to Egypt).
Currently the Green Line is not recognized as any sort of international border but, I technically live in an area on the West Bank side of the line. According to Israel, East Talpiot (my neighborhood) is a ring neighborhood of Jerusalem, just as something like Newton is to Downtown Boston. According to international law, settlements in the West Bank are illegal.
East Talpiot was established in 1973 as part of the increased building after the acquired land in the Six Day War.
Now, what does it mean that even though my neighborhood is over Green Line it is populated by Jewish Israeli's to the point where Israel considers it part of Jerusalem proper? This is what I don't know the answer to. My head, when looking at the facts relating to the boundaries and building laws, says it makes sense not to consider East Talpiot part of Israel/West Jerusalem. But it is hard to actually believe that for a few reasons. First, looking at how developed and how Jewish the area I live is, it makes it difficult to say that it is not part of Israel. My second reason I think puts things into perspective the best. Israel captured land in a war because they had a stronger military and were more equipped than their enemy. After acquiring this land as part of Israel they decided to build in an area (I'm JUST talking about where I live) where no one lived in order to make more space and more affordable housing for their citizens. If any other country besides Israel did this would they be at fault for that? Something tells me it would be a different story. Many countries have done the same thing. I cannot fault Israel for building a strong army to ensure the protection of the country in the future.

I'm going to stop here because I really don't like to get into political discussions and there is SOOO much to cover here. I am not talking, to those who want to play devil's advocate, about the right to actually have a Jewish state on the land, I'm trying just to specifically talk about the one area where I currently live, because that's where my Ulpan is. I want to be aware of what it means to me that I live on the piece of land that I do, but it is really complicated and there isn't a right and wrong answer in the discussion. Hopefully I won't be compelled to write any more controversial blog posts for everyone's sake :).