To his father, to his mother, to his brother, to his sister, he shall not make himself impure for them upon their deaths, for the crown of his G-d is upon his head (6:7)
Due to his holy status, a Nazir is prohibited from coming into contact with a dead body — even of his close relatives. However, a Kohen is also called “holy,” yet his may come into contact with the dead bodies of his close relatives. Why is a Nazir considered more holy in this regard than a Kohen?
The Shem MiShmuel answers that the difference between a Nazir and a Kohen is not in their level of holiness, but in how they acquired their status of holiness. A Kohen received his holy status through birth — the simple fact that he was born into a family of Kohanim makes him a Kohen. Accordingly, it would not be appropriate for his level of holiness to be a factor which prohibits him from acting in such a way towards his family — which was his very right to his level of holiness in the first place. However, a Nazir attains his level of holiness through choice — not through any connection with his family. As such, there is no factor to prevent the prohibition of becoming impure for them.
With this understanding, the Shem MiShmuel explains why the Kohen Gadol — despite being a Kohen — is not permitted to become impure for his family members. It is because the Kohen Gadol’s status of additional holiness did not come through his family, rather through his own merits of being the most suitable person for the position. Therefore, like the Nazir, there is nothing to prevent the prohibition of becoming impure for a family member.
The Torah is teaching us a beautiful message: Despite one’s lofty position, one must never turn his back on that which directly brought him there.
Perhaps this message is best demonstrated through the actions of Rav Yisroel Zev Gustman who was saved from the War, first by hiding from the Germans under bushes and then through eating wild berries in the forest where he fled and lived for six months. After moving to Eretz Yisroel, Rav Gustman would water his neighbor’s plants and the bushes around the Yeshiva. When the students suggested that it perhaps wasn’t befitting the Rosh Yeshiva to take time away from his learning to do that, Rav Gustman responded that bushes and plants saved his life, so he owes a debt of gratitude to them!
Even though they clearly weren’t the same bushes and plants, and perhaps not even the same species of bushes and plants, nevertheless, Rav Gustman understood the message from our Parasha; that his lofty position did not excuse him from showing appreciation to that which was the direct cause for him to reach that position.
 See the verse above together with Rashi Bamidbar 6:8.
 Shem MiShmuel in the name of his father, the Avnei Nezer: Parashas Nasso (5674).
 In fact, the story of Rav Gustman’s survival is a lot more wondrous in that he would often take walks with Rav Chaim Oizer Grodzinsky and talk in learning. On occasion, Rav Chaim Oizer would break away from the conversation and point to a plant, and tell Rav Gustman which plants were safe to eat and which weren’t; and which would provide sustenance for days and which leaves produced the most water. Not realizing the significance at the time (for he didn’t understand why Rav Chaim Oizer was telling him this information) Rav Gustman later realized that Rav Chaim Oizer, in what could only be described as ruach Hakodesh, was telling Rav Gustman exactly what he would need to survive in the forest (related by Rav Yissocher Frand).
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Regards from Yerushalayim