Fatah, the "moderate" Palestinian political movement, has admitted that it does not recognize the existence of Israel. Fatah points out that the Palestinian Authority, an organization set up in the 1990s after peace negotiations with Israel allowed the Palestinians to assume control of their own affairs, does not speak for Fatah. The Palestinian Authority recognized Israel, but Fatah points out that this was done to meet the demands of Western nations that were going to provide the Palestinians with billions of dollars in economic aid. What the Western donors ignored was the fact that Palestinians regularly used maps of the area that showed Israel as Palestinian territory. To Palestinians, Israel did not exist. Children were taught that Israel was an illegal entity, and the Israelis (at least the Jewish ones) foreign invaders who must be expelled or killed. All this was in Arabic. English pronouncements tended to be rather more opaque on the "kill the Jews" stuff.
Currently, two Palestinian factions, the radical Hamas and the much older, and more moderate Fatah, are struggling for control of all Palestinians. Both claim to represent the aspirations of the Palestinian people to have their own nation. Fatah has been at it since the 1950s. Fatah tried terrorism, guerilla operations and conventional combat, but none of these methods got them very far against the Israelis. Hamas was formed in the 1980s, as an attempt to use religion, not just politics, to expel the Jews and destroy Israel.
In the past, the Palestinian terrorists were given a pass, because the media in the Moslem world, and many parts of the West, consider the Palestinians victims of Israeli aggression and, therefore, victims no matter what they do. But now, it's different. Many Arab governments are openly criticizing Hamas for taunting Israel, and triggering the recent 22 day Israeli offensive. Even public opinion in the Arab world is hostile to Hamas, and not as sympathetic to their plight as during past Israeli military operations.
Hamas appears to have used up all its "victim" cred due to their long history of aggression, and unwillingness to negotiate in good (or any) faith. This all began back in 1994-96, when Hamas suicide bomb attacks inside Israel derailed peace negotiations with Palestinian Fatah, and began turning Israeli public opinion against the idea of a peace deal with the Palestinians. Then, in 2000, when a peace deal seemed at hand, Hamas took the lead in launching a massive campaign of terrorist attacks on Israel to derail that deal. These terrorist operations defeated after a few years, as Israel developed new tactics that kept the terrorists out of Israel. But not before Hamas carried out about 70 percent of 150 suicide bombings that killed a thousand Israelis (mostly civilians, although Hamas didn't care who they killed, even if they were Arabs, as long as it was inside Israel.)
For many Arabs, the line was crossed in 2007, when Hamas launched an attack on its Fatah rivals in Gaza. Nearly 200 Fatah members were killed. In the past, Fatah and Hamas would arrest each others people for a few days. But deliberately killing rivals was considered something only the Israelis did.
Finally, Hamas angered the majority of moderate (culturally) Arabs by attempting to impose lifestyle rules on Palestinians. This was done in the name of Islam, a Hamas effort to impose their vision of how a Moslem should live. While this plays well in places like Saudi Arabia and Iran, it was never what Palestinians believed in, nor most Moslems in general. Finally, Hamas has angered most Sunnis (who comprise 80 percent of all Moslems) by accepting military aid, and guidance, from Iran. At the moment, there is growing hostility to Shia (ten percent of all Moslems) Iran because of an increasingly hostile atmosphere between Iran (which believes it should lead the Moslem world) and Arabs (who believe Sunnis should bow to no one in terms of religion). It doesn't help matters that Iran is not an Arab country (they are Indo-European) and have dominated the region for thousands of years. Iranian encouragement of Hamas aggression is seen directed at Arabs as much as Israel.
Many Arabs, while voicing some support for Hamas, are not-so-secretly hoping that Israel will smash this arrogant, pro-Iran organization. But even if Fatah replaces Hamas, the attitudes towards Israel and the Jews shows no sign of changing.