The Integrity of the Land of Israel according to Halachah

Question: Why is it forbidden to give part of Eretz Yisrael to the Arabs?
Answer: According to Jewish Law, we are obligated to hold on to the full breadth of our Land and not to give a portion of it to another nation, on account of three reasons, each of which is sufficient in and of itself:
Saving of Lives - The survival of Israel in our Land is accomplished by the removal of the enemy’s army as much as possible, and also by a national "standing at full stature," since anything we yield brings continued pressure. For the sake of the survival of Israel, there is a need to sacrifice one’s life, as we are commanded, "Do not stand idly while your brother’s blood is shed" (Vayikra 19:16): If you see a fellow drowning in a river, or bandits are attacking him, or a wild animal is attacking him, you are obligated to save him (Sanhedrin 73a). According to various Rabbis, even if there is potential danger for the one who came to rescue, he is obligated to act to rescue one who is in a situation of certain danger (Hagahot Maimoniyot, Rambam – Hilchot Rotze’ach U-Shemirat Nefesh, chap. 1, Kesef Mishnah ibid., Beit Yosef Choshen Mishpat 426 in the name of the Yerushalmi). This is also implied by the literal meaning of the words of the halachic authorities, who mention: "One who is drowning in a river or bandits are attacking him or a wild animal is attacking him," since clearly there is also potential danger in rescuing, and the authorities did not limit the obligation of rescuing only in a rare circumstance when there is no danger. This applies all the more so when we are not discussing the saving of individuals but the saving of the entire Nation of Israel. Sacrificing one’s life is what saves blood.
The Mitzvah of the Settling of the Land of Israel - We are commanded to dwell in this Land, to settle it and to possess it, which means according to the words of the Ramban: "do not abandon into the hands of any other nation" (Positive Mitzvah #4 in additions to Rambam’s Sefer Ha-Mitzvot). This applies to every part of Eretz Yisrael (ibid.). For this mitzvah, if there is a need, we are commanded to sacrifice our lives, and even to enter into war, which is necessarily a dangerous venture. We will not attain security and peace by yielding, but on the contrary, by strength and by "standing at full stature."
Sanctification of G-d’s Name - We are commanded to sanctify G-d’s Name: "And I will be sanctified amongst the Children of Israel" (Vayikra 22:32), and there are many levels and shades of this great mitzvah (see Yoma 86a and Rambam - Hilchot Yesodei Ha-Torah, chap. 5). There is sanctification of G-d’s Name by individuals and there is sanctification of G-d’s Name by the entirety of the Nation. We are commanded to be partners in the great act of Hashem of the return of the Nation of Israel to its Land and its redemption in it, and to perform anything which is in our power for the sake of this great sanctification of G-d’s Name (see Le-Netivot Yisrael of Ha-Rav Tzvi Yehudah Ha-Cohain Kook vol.1, pp. 118-127).