I understand that the Torah orders that at the time that a Nazir finishes his year he is required to bring a Korban Chatas. I'm finding it difficult to understand this. First of all what issur did the Nazir do? The Nazir did a mitzvah by taking upon himself the nazirite oath. And secondly even if you want to find a way to say that the Nazir needs atonement, a Korban Chatas is only for someone that sins by accident, an example would be if a person forgot it was the sabbath and did one of the 39 biblical sabbath prohibitions by accident. However in this case, the Nazir knowingly and willfully takes upon himself the nazirite oath. So why does he bring a Chatas?
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The Ramban (Numbers 6:14) writes that the Nazir is sinning by leaving his elevated state, i.e. the sacrifice is for ending the state of being a Nazir.
The Rambam sees in the Nazir support for his approach that a person should not go to extremes. Shemoneh Perakim ch. 4:
In answer to your second question, accidental sin (שוגג) is not the only case of a Chatas. For example, a woman brings a Chatas after she gives birth (Vayikra 12:6).
Rashi to Bereishis 31:39 relates the word חטא to חסרון, a lack, as in the verse קולע אבן אל השערה ולא יחטיא (Shoftim 20:16).
Nefesh HaChaim in 1:6 says the same thing.
The Nazir creates a void in his closeness to Hashem by going down, and the woman has a void in her spiritual state with the loss of life from within her, and they bring a Chatas to rectify the void.
Alternatively (based on the verse from Shoftim), חטא could mean being off-target, or veering off. The Nazir brings a Chatas for veering off of the spiritual path that he is on. According to the Rambam, this could be understood as having veered off of the middle path.
Wikipedia seems to have done a good job (my emphasis)
(The Gemara, Taanis 11a, says, אמר שמואל כל היושב בתענית נקרא חוטא סבר כי האי תנא דתניא ר' אלעזר הקפר ברבי אומר מה תלמוד לומר וכפר עליו מאשר חטא על הנפש וכי באיזה נפש חטא . זה אלא שציער עצמו מן היין The possuk in bold is Bamidbor 6 (7) about the nozir.)
I think that there are two general approached to why the Nazir brings a chatas upon completion of his nezirus: