Zionism is about the Jewish people taking control of its destiny and determining for itself what kind of nation Israel should be. As a matter of principle and national honor, Israel has never ceded this right to Palestinian or other Arab leaders. Indeed, no previous Israeli government has demanded that its Arab neighbors affirm the Jewish character of the state. Israel has made peace with two Arab countries — Egypt and Jordan — without including such a demand in the terms of the agreements.
The task of Israel’s government is not to gain “recognition” of its Jewish character from anyone, friend or foe. Its job is to guarantee a stable Jewish majority that will enable the Jewish state to continue to develop and evolve in a democratic fashion as well as to ensure Israel’s Jewish character for the future.
This a version of what I call left-wing machismo speak. It takes the form of "are you saying Israel needs Arabs to affirm its identity? No way! Israel is way tougher than that -- it doesn't need nothin' from nobody!"
I'm not opposed to left-wing machismo as a rule -- it does serve as an important counterweight to the sentiment that the only way to show toughness is through conservative belligerence (policies which, often times, are actually demonstrations of weakness, not strength). At the same time, the hyper-separatist tenor of this claim rings a false note to me. It does matter how Israel's neighbors think of it, and whether or not they view it as a legitimate state. Peace is the first priority, obviously, but ultimately I want more than peace, I want mutual respect -- and I highly doubt that peace will survive without respect anyway. Acting as if we can split these two issues apart -- that both sides can fundamental view the other as interloping thieves without damaging the longevity of a peace deal -- strikes me as tremendously naive.