If they did not want war, WHY did they demand the REMOVAL of the UN forces????

"The decision on May 13, 1967, to remove UNEF and deploy UAR troops along the Israeli border was subsequently made to strengthen his position throughout the Arab world. It is doubtful that Nasser intended his actions to provoke a war with Israel, yet the alternative--losing prestige and influence throughout the Arab world–was deemed even less palatable.

The message to withdraw UNEF was first conveyed to the commander of UNEF, Major General Indar Jit Rikhye, on May 16, 1967. The UAR Liaison Officer, Brigadier General Ibrahim Sharkawy, called Rikhye in the afternoon to inform him that a special envoy would be arriving with an important message for the UNEF commander. The letter--delivered by a courier holding the rank of brigadier general--was from the UAR Chief of Staff, Lieutenant General Muhammad Fawzy, and simply stated:

I gave my instructions to all UAR armed forces to be ready for action against Israel, the moment it might carry out any aggressive action against any Arab country. Due to these instructions our troops are already concentrated in Sinai on our eastern border. For the sake of complete security of all UN troops which install outposts along our borders, I request that you issue your orders to withdraw all these troops immediately.[11]

The courier, expecting immediate compliance on the part of UNEF, was sorely disappointed when General Rikhye merely noted the contents of the letter, and informed his visitors that he would pass the message on to Secretary-General U Thant. Rikhye would have to await orders from New York.

Clearly troubled by the lack of immediate action, the envoy explained that UAR troops were already on their way to the international frontier and wished to prevent any clashes with UNEF. From the UAR military point of view, it was imperative that UAR forces occupy Sharm al-Shaykh and al-Sabha before the Israelis had a chance to react. Rikhye was adamant in his inability to act before receiving instructions from New York, but ventured to ask his interlocutors if the consequences of removing UNEF from the international frontier had been fully contemplated. To this Sharkawy responded, "I will see you for lunch at the best restaurant in Tel Aviv in a few days."[12] "

http://meria.idc.ac.il/journal/2005/issue2/jv9no2a5.html