They usually say that Israel would be perfectly allowed to build such a fence on the Green Line itself, but not to protect Israelis in who live across it even in areas that would never be part of "Palestine."
Well, it turns out that the Green Line is not so sacred to them when they don't like it.
Ma'an reports:
Battir is a Palestinian village southwest of Jerusalem famous for maintaining a Roman-era terraced irrigation system in continuous use for nearly 2000 years. The Hejaz Railway, an Ottoman-built track originally running from Damascus to Medina, winds through the valley intersecting the village.This means that Israel is planning to build the barrier on the Green Line itself, exactly what its critics say they want - when it suits them. If a State of Palestine is created along the Green Line as the Arabs insist it must be according to international law, this is what would happen to Bittar anyway - which, incidentally, is the ancient Jewish village of Betar.
Israeli authorities subsequently drew the Green Line along the tracks of the Hejaz Railway, tearing apart the village and leaving 30 percent of Battir's land on the Israeli side of the Green Line. [Jordan and the UN had a bit to do with drawing the Green Line. - EoZ]
However, after 1948 Battir residents struck a deal with Israeli authorities, allowing them to cultivate their lands over the Green Line in exchange for protecting the railway. This deal held even after Israel occupied the West Bank in 1967.
Israeli authorities are currently planning to build the separation wall through the village, effectively confiscating 30 percent of the lands and cutting across the village's ancient terraces.
The fact is that the Green Line split a number of Arab villages. During the 2008 negotiations, the Israeli side suggested that splitting Arab towns along the Green Line - Beit Safafa, Barta’a, Baqa al-Sharqiyeh, Baqa al-Gharbiyyeh - is unacceptable and suggested that they get incorporated into the Palestinian Arab side as part of a land swap. Al Jazeera slammed the suggestion because Arab Israelis would become citizens of the PA! To them, the Green Line must split the villages when Israel suggests otherwise.
And then Israel would be blamed for that, just as this Ma'an article blames Israel and Israel only for drawing the Green Line to begin with!
To the Israel haters, the Green Line a sacred boundary only when it can be used to hurt Israel, even at the expense of "Palestine."