The proper precedence
…אשה כי תזריע וילדה זכר וטמאה שבעת ימים וגו’
…when a woman gives birth to a boy, she shall be spiritually impure for seven days…
At the end of the previous parsha, there were many details related to the spiritual impurity imparted by animals. This week’s parsha begins a long series of laws related to the spiritual purity and impurity of humans. Seemingly, the order is backwards. Since mankind is the principle player in the Torah, shouldn’t their laws come first? That which is primary takes precedence over what is secondary. Why then are the laws of animals taught first? Rashi addresses this, by reminding us that in the Torah’s description of creation, first the animals were created, and only then mankind. Just like the animals preceded Man during creation, their laws of impurity are taught first.
However, this seems to exacerbate the question. If mankind is primary, why were they created last? Wouldn’t it have made sense to create them first? Actually, Chazal inform us of four reasons why this was so. One is that it was to teach us a lesson. Although mankind has dominion over the animals, we must not to become haughty, because even a mere mosquito was created before Man. Second, because of Man’s prominence, if they had been created first, it could have looked like Hashem needed a partner to help with the rest of creation. Third, by creating Man last, it enabled that they could partake of the mitzvah of Shabbos right away. Finally, it was so that all of Man’s physical needs would be readily available for the taking.
The problem is none of these reasons apply in our parsha. These reasons explain why the animals were created before mankind, but if it was for these specific reasons. Why should that have any bearing on whose laws of impurity should be taught first? It would still seem more reasonable for the laws of impurity for humans to precede that of the animals. Why then did the Torah teach the laws of impurity of animals first?
Rashi’s answer in fact tells us all that we need. The laws of humans and animals, how they should behave or be related to, is something similar to their creation. Just like their creation was the refinement of their form, their laws are the refinement of their existence. The Torah’s laws gives them purpose and boundaries. Therefore, just like the Torah preceded the creation of animals to humans, so too with their laws. This is because the laws of their behavior are the completion of their refinement.
Chazal explain why in the six days of creation, each day is counted “one day”, “a second day”, “a third day”, but the sixth day is counted “the sixth day”. It’s to allude to another sixth day, namely the sixth of Sivan, when the Torah was given. This is to teach us that Hashem made a stipulation in the entirety of creation. The universe was in a state of limbo until that day. If the Jews would accept the Torah, then great. If not, then everything would return to complete nothingness.
This holds true because of what we just said. The six days of creation weren’t really completed until the giving of the Torah. The Torah contains the laws which refine mankind and the rest of creation. If the Torah wasn’t accepted, everything wouldn’t receive its necessary refinement. This makes it that the very laws of the Torah are considered part of creation. It makes sense then that the laws of impurity of our parsha would follow the order of precedence chosen during creation.
 Based on Gur Aryeh to Leviticus 12:2 § 1
 Leviticus loc. cit.
 Ibid Chapter 11
 To ibid 12:2, quoting Vayikra Rabbah 14:1
 Genesis 1:20-25
 Ibid v. 26-31
 Sanhedrin 38a
 See Chiddushei Aggados ad. loc., where the Maharal gives a deeper explanation behind all of these reasons
 Rashi ad. loc.
 See Rashi to Genesis 1:25 and Ramban to ibid v. 7
 Shabbos 88a, brought by Rashi to Genesis 1:31
 Genesis 1:5
 Ibid v. 8
 Ibid v. 13
 Ibid v. 31
 Shabbos 86b – 87a presents a dispute as to when the Torah was actually given. This explanation of Chazal follows the opinion of the Sages, who say that the Torah was given on the sixth of Sivan. Rabbi Yossi however disagrees, and says the Torah was given on the seventh of Sivan. Tangentially, with regards to their underlying dispute, we happen to rule like Rabbi Yossi (Shulchan Aruch Yoreh Deah 196:11). This creates a contradiction, as we observe Shavuos on the sixth of Sivan, like the opinion of the Sages. See Magen Avraham 494:1 and Beis HaLevi to Exodus Chapter 19 s.v. להבין, who offer interesting resolutions to this contradiction. See also Tiferes Yisroel Chapters 25, 27, who discusses this topic at length