The same reason that Italy should be an Italian state, and Germany should be a German state, and Russia should be a Russian state.
Peoples are entitled to self-determination. It's in the UN charter.
A democratic and Jewish-majority Israel living alongside a democratic and Palestinian majority Palestine (aka the "two state solution") is the only outcome that would fulfill the national aspirations of both peoples. Part and parcel of that is Israel as a Jewish state, and Palestine as a Palestinian state.
A lot of the objection to there being a 'Jewish state' comes from a fundamental misunderstanding of the nature of the Jewish people. This can be seen in another diary currently on the rec list:
Asking Palestinians to recognize Israel as a “Jewish state” has been likened to asking American Jews and other non-Christians to officially recognize the United States as a “Christian state.”
This would be the case if the Jewish people were a religious classification. However they are not. The Jewish people are, in fact, a people. Many of them practice the religion of Judaism, but many do not. In fact, Israel has one of the highest proportions of atheiests and agnostics in the world. A majority of Israeli Jews identify as "secular".
Israel is a largely secular state, with some religious influence in government. The same could be said about the US, by the way. However, and this is crucial, a Jewish state does not mean a state of the Jewish religion, but rather a state for the Jewish people - an ethnic and national homeland like most nations in the Old World.
There is the objection that in order to maintain the Jewish character of Israel, the so-called 'right-of-return' of the descendents of refugees from the 1948 war will have to be relinquished. This is simple demographic fact. Is that unfair to the descendents of people who were uprooted in that war? Yes it is.
However, the history of the I/P conflict is riddled with unfairness. If the Arab side would have accepted the 1938 or 1948 partition plans, there would have been no refugees (other than possibly the 700,000 Jews who were driven from Arab countries - where is their right of return?). It was only because the surrounding nations invaded that there was a war in 1948. I also point out that the surrounding nations could have established a Palestinian state in the entirety of the West Bank and Gaza including most of Jerusalem anytime between 1948 and 1967, and could have avoided the occupation entirely had they not gone to war in 1967.
In any case, the past is done, and there were injustices on all sides. The most just way forward is who states for two peoples, living side-by-side and not in conflict. And the only way to achieve this is with Israel as the state for the Jewish people and Palestine as the state for the Palestinian people.