Israel took East Jerusalem from Jordan in 1967 and has held it since. The area is considered to be the capital of the would-be Palestinian state and, thus, is a source of constant conflict. However, Israel holds the territory. Until such time that Israel surrenders it, Israel is correct to build there.
Israelis are completely justified in building new settlements in East Jerusalem. Israel was the home of the Jewish people long before others settled there. Today, the government is an Israeli government and those who do not agree with the regime in power should either leave the country or work to change the government from within. East Jerusalem falls within the country's legal boundaries, and therefore, the citizens of the country have the right to settle there if they choose.
East Jerusalem belongs to Palestine. It is Palestinian land, it is where the Arabs live and Israel has no right being there. The land was illegally taken from the Arabs in 1967 and should be returned. And many archaeologists believe that the Arabs may have arrived in Palestine/Israel around the same time as the Jews. And if you think the Palestinians should leave, well then where would they go!