Abbas' Antisemitic rant provides an opportunity for Israeli outreach

Palestinian Authority President Mahmoud Abbas--sometimes known as Abu Mazen--is an anti-Semite. His racist remarks denying Jewish connection to Israel and blaming us for our own extermination at the hands of the Nazis should come as a surprise to nobody. This is a man who wrote his doctoral thesis on Holocaust denial. What is important is that the winds of destiny are changing.
The Palestinians are weaker, economically and politically, then they ever have been, with eroding support even among Middle Eastern countries. The European Union and the United Nations---traditionally pro-Palestinian entities---have even condemned his latest remarks. Abbas, with all of his stupidity and lack of strategic thinking, is only alienating himself and the Palestinian people by making Israelis more skeptical of a peaceful two-state solution (and more right-wing, consequentially). But this provides an opportunity for Israel--and Diaspora Jews--to address some concerns held by the Palestinian community and their backers. 
One should be, with the 70th anniversary of the 1948 War of Independence approaching, to recognize the pain felt by Arabs (Palestinian and otherwise) surrounding the events of the end of British Mandatory rule. Some scholars and peacemakers believe that the founding national narratives of Israeli Jews & Palestinians are the Holocaust and "The Catastrophe" (al-Nakba), respectively. While the national narratives of Israeli Jews & Palestinians are more complex than that, these are certainly important events in the narrative that require mutual respect, understanding, and compassionate listening.
But just as "the Arab side" hasn't, generally speaking, seemed to absorb the enormity of the Holocaust and its meaning to the Jewish people, Israel and its supporters often haven't reciprocated in the case of al-Nakba. There has been too much denial of the event, or defensiveness, when there instead should and could be more listening and compassion. Just as many Arabs try to "lecture" Jews on the "truth" about the Holocaust or Jewish refugees from Islamic lands, the same can be said of Jews "lecturing" on the truth of al-Nakba. We cannot expect their side to do what we can't when it comes to hearing our pain and accepting certain difficult truths.
It's true that many of Mandatory Palestine's Arab populations voluntarily left & sold land to Jews(often for more than it was worth), sensing that a new and violent era was beginning, and that the old Palestine was no more. Others were encouraged by Arab regimes to abandon their homes and return after the Jews were "thrown into the sea." Eventually, others also left the land due to other reasons, such as educational and economic opportunities elsewhere.
The Palestinians & their sympathizers--especially other Arab countries--need to accept this instead of only blaming Israeli Jews. Arab countries should apologize for their role in al-Nakba as well, and the subsequent persecution Palestinian refugees have faced in their lands.
But some were indeed forced by Israeli forces from their lands or even murdered, as in the case of Deir Yassin. The Israeli Arab population shortly after the War of Independence lived under military rule for years, and there is still some level of discrimination against them today.
It's true that the Holocaust and al-Nakba cannot be compared. First of all, the Holocaust was an attempt to wipe out all of Jewry. "The Catastrophe" was a result of war, much like what occurred with Indian Partition or the Ottoman-Greek Population Exchange. Secondly, tragedies can't really be compared because the communities that undergo them feel differently and more deeply than even the most sympathetic allies. But there is room for more understanding and respect, on both sides, of both tragedies. Only after this sort of bicommunal reflection--as must be done in Cyprus, Northern Ireland, Rwanda, and other such places--can true peace flourish, between capitals and between ordinary people. 
Some Israelis and Jews often complain about the "unfair burden" placed on them to make peace with a leadership or people who, often times, seem unwilling to do so. Others bring up the "soft bigotry of low expectations" held by Westerners--that the Palestinians and their allies are seen as less civilized, and so the same standards are not applied to them as they are to Jews/ Israelis. While this is indeed a concern that must be addressed and remedied, it by no means gives us the excuse to ignore our own shortcomings. We, as a people, should hold ourselves to a higher standard than the likes of Abu Mazen, and as expected of us, reach out for peace. Let us put the onus on the Palestinian Authority to accept our right to exist and make peace. There are many Palestinians who will hate us regardless of what we do, will never accept our rights in the land, and will never want to make peace. In every conflict, on all sides, there are such people. But there are also people--including Palestinians--who do accept our grievances, or who are willing to hear them out if they also feel they are heard and respected. 
Peace with the Palestinian leadership is currently impossible, for a number of reasons. While the Likud government makes it harder in some ways, the underlying issue is the rejection of the Palestinian leadership (and many of its subjects) to hear the Israeli narrative and accept Israel as the national home of the Jewish people. People-to-people peace, in some ways, is the more realistic path forward for the time being. Allowing the Palestinian narrative of al-Nakba to be heard and apologize for the Israeli role in it is a step in that direction.
That doesn't mean Israel should apologize for its existence. It also doesn't mean we shouldn't demand that the Palestinians don't recognize our own traumas (the Holocaust, the persecution and expulsion of Jews from Islamic lands, etc.). It should not mean that Israel accepts Palestinian refugees back into the country or surrenders Jerusalem. But it is important that we show the international community that we hear out the Arab narrative and concerns and try to make amends to leave the option of wider peace open, and to distinguish ourselves from the likes of Abu Mazen. It will also send an important signal to Arab countries that are making similar signals of openness to Israel. 
Ignoring trauma--let alone creating it--internally poisons a society. In the United States, the whitewashing of atrocities and genocide committed to the Native Americans (and other minorities, via different forms of oppression) has led to infighting among Americans and a loss of national cohesion. In Turkey, the denial of the 1915 genocide of Armenians, Greeks, Assyrians, and others has led to continued tensions with Armenia and its diaspora over a century later. Arab countries (Libya, Iraq, Yemen, etc.) that expelled their Jews have largely disintegrated.
The sooner that Israel recognizes the plight of its Arab community and certain aspects of the Palestinian narrative, and takes some steps towards fixing or apologizing for these acts, the healthier it will be internally, and the less isolated it will be. It will also cause the Arab community in Israel, as well as abroad and in the Palestinian Territories, to do some soul searching in regards to hearing out the Jewish narrative and grievances, and lead to international pressure on the PA and other such entities to reciprocate.