The goat
sacrifice brought on New Moon atones for the cases of ritual impurity
which never become known to the person who was impure. That is why this
sacrifice is called “a
sacrifice for God” - for God alone knows of this impurity - these
are the words of Rabbi Yehudah.
Additionally, as Resh Lakish explained, God said, “This he-goat shall be
an atonement for something that I did.” When God created the Sun and
the Moon, they were initially of the same size. The Moon complained that
it is not appropriate for two rulers to rule at once, and God said,
"You are right. Go and make itself smaller." The Moon then reasoned that
it was unjust that it should suffer just because it raised a valid
point. In order to placate the Moon, God promised that the Jewish people
will be bringing a sacrifice for God's sin, as it were, on every New
Moon.
Art: Caspar David Friedrich - Man and Woman Contemplating the Moon