What is "Israel"?
The word "Israel" means a few different things.
Historically the word has been used to mean "the collective body of Jewish people".
It also refers to a Jewish nation that existed long ago.
Today the name is used by a country in the Middle East. That country was founded by Zionists who chose to use the name "Israel" to give the appearance of continuity to their state.
Most importantly, "Israel" refers to the Land of Israel. This is simply... the Land of Israel. It comes without any political baggage. Just land. The Land of Israel is always the Land of Israel, regardless of who has political control at a given moment.
Jews vs. Muslims?
One of the biggest myths surrounding the Middle East is that there is some inherent conflict between Judaism and Islam.
The truth is that Jews and Muslims got along fine in the Land of Israel until the State of Israel was formed.
A big part of the "War on Terror" is the fantasy that there is some inherent primitiveness in Muslims, or in Islam, that prevents Judaism and Islam from coexisting. In fact every religious group has extremists and Islam has no more or less than Judaism or Christianity.
Ideologically Jews and Muslims get along better than either has gotten along with Christians.
Christians are an important political ally to Zionists, but Christianity is ideologically offensive to Jews. Likewise, Muslims also take offense to Christianity (while they do not to Judaism).
In strictest terms, A Jew respects only Judaism. A Christian respects Judaism and Christianity. A Muslim respects Judaism fully, but respects Christianity as a "flawed religion" (Muslims feel Jesus was a prophet, rather than a deity). That is clarified well by Wikipedia at http://en.wikipedia.org/wiki/Jesus_in_Islam.
One of the biggest projects of the modern state of Israel has been to reframe the western religious view to portray Islam as a violent, primitive religion and to portray Judaism and Christianity as natural allies against this "threat".
Why isn't there a Palestinian state?
There are several schools of thought among Zionists (supporters of the current State of Israel). The prevailing strategic view is that the more Israel (the state) gets developed, the more marginalized and insignificant will be those people who have claims against the state. The state of Israel has hooked onto the paradigm used to develop America (against Native Americans), even to the extent of using words like "settler" and "territory" etc.
In other words, many Zionists believe that if they can prevent the Palestinians from getting any land for just a few more decades, eventually the Palestinian cause will seem to "fade" as happened with Native Americans.
One of the most important strategic efforts of the state of Israel has been to promote the idea that Islamic extremism is a growing phenomenon. The suggestion is that there is something "defective" about the Islamic religion that necessarily causes extremism.
In fact, in any society or group with a stable religion there is invariably a progression towards moderation and even secularism. Common sense and experience tells a person that a group of people do not become more radical in their religion as time passes, unless there is another pressure (e.g. political) driving that radicalism.
The significance of this is that Islamic "extremism" is being used to protect an agenda. There is one central issue that creates a problem for the state of Israel. That issue is the fact that the state of Israel was built by taking land away from people who had lived on that land for many generations. The pretext of "Islamic extremism" was carefully developed and has been obscuring the actions of the state of Israel for decades.
It is necessary though to also view Israel in the context in which it was formed. Antisemitism in Europe was severe in the time before the state of Israel was formed. European Jews did need a safe haven.