Wikipedia says "Purim is a festival that commemorates the deliverance of the Jewish people of the ancient Persian Empire from Haman's plot to annihilate them."
Judaism 101: "It commemorates a time when the Jewish people living in Persia were saved from extermination. "
Jewish Virtual Library: "It commemorates a time when the Jewish people living in Persia were saved from extermination."
Notice what Purim isn't. It is not celebrated as a military victory. Jews aren't celebrating the death of Haman and his allies. While Haman's death is an integral part of the Purim story, and it was necessary for him to die in order for his decrees to be countermanded, we do not specifically cheer Haman's death except as to its role in the salvation of Persian Jewry. From Judaism's perspective, it would have been preferable if the Jews had not been in danger at all (and if they would have repented on their own and not as a result of the direct threat to their lives.)
Purim is a joyous holiday in that it does not celebrate death, but the saving of lives.
Sometimes, war is necessary and lives have to be lost for others to be saved. Arabs tend to celebrate the (real or perceived) defeat of their enemies, and they assume that Jews are doing the same thing on Purim and Chanukah (and Yom Yerushalayim and Yom Ha'atzmaut.) This is exactly wrong: the Jews are celebrating their survival and, yes, their victory - but not the defeat of their enemies. The two are obviously related but the mindset is completely different.
One celebrates life and the other celebrates death.
Chanukah represents a spiritual victory more than a military victory; Yom Ha'atzmaut represents the revival of a millennia-old dream of Jewish nationhood on its own land; Yom Yerushalayim celebrates the return of Judaism's holiest city to Jewish control. All of these events would have been preferable had no blood been shed. The defeat of enemies is not what is being celebrated; that is a necessary evil, not a cause for cheer.
Though of course Jews take undeniable pride in military victories, they would prefer that the engagement never happen to begin with.
Arabs cannot wrap their minds around this idea. For them, military victories are proof of their manhood, a source of "honor," and, for Muslims, proof of their belief system being superior. Conversely, military defeats are shameful and indicate a problematic belief system, as why would Allah allow his people to be so dishonored? The point is the utter defeat - and more importantly, the humiliation - of their enemies.
This is why Arabs cannot understand Purim, and they cannot understand Jews. They project their own belief system and the honor/shame culture on their enemies. They cannot conceive that the defeat of one's enemies is not the overriding goal of an embattled and surrounded people. All of the vitriol heaped on "Zionists" about their supposedly racist and genocidal goals is nothing more than Arab projection of their own belief system on Jews.
And, as Adin Steinsaltz notes, there are only two ways for Jews to counter the anti-semitism of both Haman and Hamas:
The conclusion of this is that we only have two possible responses. First, we can do our best, as was done in the days of Esther and in other generations, to defend ourselves against evil and fight it. This needs to be done in any case, even if only to gain a respite from the outbreaks of hatred.This is what Purim is about - celebrating Jewish survival. Our enemies' defeats are incidental, and eventually comedic, but they are not central.
The second possibility is to laugh. Laugh not only about the defeat of our enemies, but also about the absurdity, ridiculousness, and inherent contradictions of anti-Semitism. The laughter does not mean that there is an answer, yet this is our way of declaring that we have removed ourselves from the irrational interaction of hating Haman. We laugh at Haman, Ahasuerus, and all their successors, because after all we shall prevail and stick around, and they shall become the subject of jokes.