Israel is important to Jews because God promised it to Jacob (Genesis ch.28), the father of the Israelites, and his descendants. Jacob was renamed Israel by God (Genesis ch.35); and the Israelites lived in Israel during the era of the Patriarchs (220 years), during the era from Joshua until the First Destruction (850 years), during the Second Temple era (420 years) and afterwards. They remained a majority in the land for another 300 years after the Second Destruction; and a minority of Jews remained there throughout the ensuing centuries.
Israel had been the site of the First Temple, built by King Solomon; the dynasty of King David; the Second Temple, built by Ezra; and the Hasmonean Dynasty. It was where the Hebrew Prophets lived, and where the Mishna (Oral Torah) was codified. Also, many of the Torah's commands apply only in Israel.
See also the other Related Links.
The way the question is written is to assume that it is not theirs, which is not the case in the slightest. Nobody asks what "entitled" Poles to create a nation-state in Prussian, Russian, and Austrian land or what "entitled" British colonists to create a European-Style country in North America. The people who live in a certain area and have a connection to that area have an intrinsic right to that land. The Jews are no different as concerns Palestine.
According to historical, religious, legal, and political grounds, the territory of the British Mandate of Palestine at least partially, if not entirely, belongs to the Jewish people.
1) Historically: The Jews have an undeniable presence in the land from at least 700 BCE until 70 CE and this is proven not only by the Biblical account, but from Assyrian Ruins, Babylonian documents, Hellenistic inscriptions, and Roman volumes. Jews had a continuous presence in the land from 70 CE until the present day (even though they were nowhere near the majority) even though they were forcibly deported from the territory. The fact that they survived, as opposed to the Arameans or Hittites who were similarly exiled does not illegitimate their claims.
In addition to the population-part of the historical claim, Jews have physical ruins and cities that are very sacred to them in the territory of the British Mandate of Palestine. The city of Jerusalem is mentioned over 700 times in the Jewish Bible. The city of Nablus used to be the Northern Metropolis of Shechem. Hebron was the first capital of Ancient Israel whence Saul ruled and David ruled until he conquered Jerusalem from the Jebusites. Even more recent sites like Masada document the Jewish presence and struggle to persevere.
2) Religiously: The Jewish claim to have a connection to the land of the British Mandate of Palestine is firmly grounded in their religion. Jews as early as the Babylonian exiles wrote about returning to the land because God had promised it to them. According to the Pentateuch, God promised Abraham that piece of land. (This promise is even acknowledged in the Qur'an 5:20-21, 17:104, and 26:59.) Many Jewish Holy Sites are in Israel such as the Kotel Hama'aravi (Western Wall).
3) Legally: By international law, the Ottoman Empire took the territory from the Seljuks and Abbassids by internationally recognized conquest. The territory was ceded to the British as a Mandate by the Ottomans as a term of surrender in World War I. (Even though the British had promised the territory to both the Arabs and Jews during the War, neither promise is legally binding.) According to the terms of the Mandate, even though the British were in control, the League of Nations had official jurisdiction. In 1947, the British gave direct authority to the League of Nations' successor, the United Nations, in accordance with the terms of their Mandate. The UN passed the 1947 Partition Plan that gave both a Jewish State and an Arab State the Right to Declare Statehood. The fact that the Arabs decided not to immediately declare such a state does not make the Israeli declaration any less valid. (It is important to note that Palestine did declare statehood on these grounds in 1988, which further cements the legality of this view.)
4) Politically: Jews invested a lot in building the political and physical infrastructure of the land even before they had control. Jews built farms, trained military brigades, created political parties, studied government, and defended themselves. This created a system that was able to repel the Arab Attacks in the Arab-Israeli War of 1948-9, secure expanded borders in the Six Day War of 1967, and hold those borders in the Arab-Israeli War of 1973. Israelis were actually able to exert control over this territory.
Of course, this list is not exhaustive, but should capture the sentiment of the question.
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