The Mishnah in Makos (2:6) tells us that when one kills his fellow man by accident, he must go to an ir miklat and live there until the kohen gadol dies. This prompted those in the arei miklat to daven that the kohen gadol should die, so they could go free. Therefore, the Mishnah writes, "The mothers of the kohen gadol would supply the [people in arei miklat] with clothes and food, so they won't daven that their children die."
The Gemara (Makos 11.) wonders why the mothers are concerned about their prayers, since the kohen gadol did nothing wrong. It wasn't his fault that these murderers ended up in arei miklat. So, why was the kohen gadol's mother afraid of their tefillos? Their tefillos won't cause any harm, because the kohen gadol is innocent! The Gemara answers that the kohen gadol is, in fact, responsible "because he should have davened for his generation [that even accidental murders shouldn't occur], and he didn't daven."
(The Gemara brings an incident about a person who was eaten by a lion. This occurred three parsah away from where Reb Yehoshua ben Levi lived. Eliyahu HaNavi would often come to Reb Yehoshua ben Levi, but after someone was killed, three parsah away from Reb Yehoshua ben Levi, Eliyahu didn't come to him for three days. Reb Yehoshua ben Levi was held responsible for the death because he should have davened that such accidents shouldn't occur in the area where he lived.)
Based on the above ideas, the Meshech Chachmah (6:8) explains that this is the reason a nazir must bring a korban chatas if someone dies in his presence. What sin did the nazir commit, that he needs to bring a korban chatas? The Meshech Chachmah explains that the nazir should have davened that people shouldn’t die around him. Therefore, if someone died around him, he is responsible for the death, similar to Reb Yehoshuah ben Levi and the kohen gadol, who were responsible for the deaths that occurred.
The Kli Yakar writes that the reason for the korban chatas is that the nazir was unhappy with his nazirus and regretted the restrictions he had placed upon himself. The proof that he isn't happy is that he has become tamei. The Kli Yakar explains, "If he were happy with his nazirus, he would be extra careful to avoid tumah. However, he wasn't cautious, proving that he wasn’t so happy with his nazirus."
This is human nature. When you are happy about a situation, you are more cautious. If the nazir were happy with his nezirus, he would have been extra careful, and he would be a zariz to leave before anyone dies. The fact that he became tamei shows that he wasn't happy with his nezirus. His lack of joy for this mitzvah is his aveirah, for which he brings a korban chatas.
One doesn’t need to become a nazir to attain this great holiness. Whenever one refrains from indulging in unnecessary worldly pleasures, whenever one has prishus, he becomes extremely holy.
