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You said, "We left Gaza with land borders under Egyptian and Palestinian Authority control."
That is not true. "Borders" plural is actually "border" singular, and that is the one with Egypt. When Israel "pulled out" it left the Israeli Gaza Strip barrier, a separation barrier built by Israel that completely encircles the Gaza Strip, and is constructed of wire fencing with posts, sensors and buffer zones on lands bordering Israel, and concrete and steel walls on lands bordering Egypt.
The opening in this barrier into Egypt is at Rafah and that opening was under the administration of the European Union because Israel did not want the Palestinians to control any part of it. However, Israel still had enough control over it to have it closed during its blockade of Gaza.
The Gazans mainly led by women broke through that barrier in January 2008 and Gazans streamed through into Egypt to buy food and supplies and weapons. However the Egyptians have reestablished control on their side. The European Union have withdrawn their guards from the Gazan side of the crossing so now there is defacto Palestinian control on the Gazan side. But it was not something that Israel "left" or wanted to leave to the Palestinians.