Some (secular) reasons that Israel has a right to exist:
Israel was created by a UN vote, not by a treaty between imperialists like most other nations in the Middle East. Whatever one may think of the UN, it is the only expression of the general will of nations.
Israel defended her territory in multiple defensive wars. Israel did not take territory from other nations in wars of aggression. The majority of Israelis have always been prepared to trade occupied territories for peace and normal relations with her neighbors.
Israel reclaimed what had been worthless land and built an economy that could support a population of millions in a place that has been called “the armpit of the Ottoman Empire”.
The Jewish people began creating the institutions of the state in the beginning of the 20th century long before WWII, in order to exercise their natural right of self-determination. The state would have come into being whether or not there had been a Holocaust. It is not in any way justified by the Holocaust.
Israel is a democracy. It is not a monarchy or dictatorship like most other nations in the Middle East. Therefore it is one of the only middle-eastern nations to legitimately exercise power over its inhabitants.
Israel is the only nation in which the Jewish people can exercise their right of self-determination.