ציטירנדיקער פּירוש אויף במדבר 12:5

It is possible to understand the reason for this offering as not so much related to her as to her “mother,” i.e. the first woman Chavah, who had committed the first sin as a result of which all women subsequently had to endure painful deliveries, pains of menstruation, separation from their husbands, etc. Had Chavah not been guilty of introducing disobedience to G’d’s command women would have been spared all this. The whole process of giving birth would have remained as natural a process as for trees to yield their fruit. Trees do not have to experience desire in order to become fertilized and to yield their fruit year after year. This woman who gave birth now may be perceived as the branch of a contaminated root, daughter of a corrupted mother and as such some of the mother’s contamination was transmitted to her. Hence the Torah requires that she atones for this by bringing a sin-offering after giving birth. By doing so she does her part in helping to atone for the original sin of Chavah.
In fact, we find that we are taught in Shabbat 31 that women have been commanded to observe three commandments specifically to help undo the spiritual damage caused to the species of man by their original “mother.” They are 1) the observance of a state of impurity with subsequent purification during their regular menstruation cycles. 2) חלה, the separating (and while the Temple was standing giving to the Priest) of the first part of any dough they bake from the five species of grain (Numbers 15,20-21), and 3) the lighting of the Shabbat candles every Friday night. [The last two commandments devolve on the male when there is no woman at hand. Ed.] In fact, according to the Talmud there, failure to observe these three commandments meticulously may result in their dying during childbirth. Seeing that that particular sin was preceded by the sinful thought before it was actually carried out, the woman offers both a burnt-offering and a sin-offering after giving birth; the first offering atones for the sinful thought and the second for the sinful deed (compare verse 5). This is the reason the Torah wrote of the requirement for the woman to bring a burnt-offering before mentioning the need for her to bring a sin-offering. In all other instances where the sin-offering has to be brought on account of a sin committed by the person bringing the offering, the Torah demands that he first cleanse himself spiritually by atoning for the deed before bringing the burnt-offering.
When the Talmud Zevachim 90 states that when the Torah wrote the words אחד לעולה ואחד לחטאת, “one as a burnt-offering and one as a sin-offering,” (verse 8) that the actual presentation of these two offerings does not follow the order in which the two offerings are listed here, this supports our contention that the reason the Torah reversed the order in which the legislation is written is meant to teach us the lesson we mentioned, i.e. that the sinful intention preceded Chavah’s eating of the fruit of that tree, i.e. the offering we speak of here was not in penitence for an unintentional inadvertently committed sin as are most other sin-offerings.
According to the opinion of our sages (Niddah 31) the reason for the sin-offering the mother has to bring is that she presumably was guilty of swearing off marital relations with her husband seeing that the experience of giving birth was so painful and the pregnancy so uncomfortable. Her offering atones for such a lapse on her part. Seeing her oath at the time was due to her being in pain, and she is not a free agent allowed to deny her husband his marital rights, she has committed a culpable sin, i.e. she needs to atone with a burnt-offering for her sinful intent.

והענן סר מעל האהל, “and the cloud departed from above the Tent.” If the Torah referred to the cloud which had descended onto the entrance of the Tabernacle in verse 5, the Torah would now have had to describe it as “the cloud departed from the entrance of the Tent.” Seeing that the word מפתח is missing, we must assume that the cloud the Torah speaks of is the one which always signaled that the people should either move or make camp. Seeing the cloud departed the Israelites thought that they were meant to break camp and start moving. However, G’d commanded them to wait for seven days. This is the meaning of the words תסגר שבעת ימים, “let her be quarantined for seven days” (verse 14). When the Torah reported afterwards that the people did not journey this is equivalent to saying that the cloud had not actually traveled away from the Tabernacle any distance at all. It only departed to show that ordinarily, if not for Miriam’s quarantine, the people would have been on the way already. In other words, the Torah made it clear to everyone that the entire people’s progress toward the Holy Land had been delayed for seven days in honor of Miriam.

AND THE ETERNAL APPEARED IN THE TENT IN A PILLAR OF CLOUD. The purport thereof is that the pillar of cloud was over the entrance [of the Tent] and G-d appeared in the Tent — this being the Glory, according to Rabbi Abraham ibn Ezra. In my opinion, this verse is like And the Eternal came down in a pillar of cloud, and stood at the door of the Tent;¹⁹Ibid., 12:5. and, behold, the Glory of the Eternal appeared in the cloud.²⁰Exodus 16:10. And the meaning [of the verse here] is that He wanted to speak with Moses so that Joshua would hear, and He would also charge Joshua there. Now, to Moses it was said, And there I will meet with thee, and I will speak with thee from above the ark-cover²¹Ibid., 25:22. but Joshua was not of that exalted status [in prophecy] and he was forbidden to enter the Tent altogether. Thus the phrase, and the pillar of cloud stood over the entrance of the Tent²²In Verse 15 before us. reverts to explain that the cloud, in which was the Glory, was above the door of the Tent covering it, and accordingly He was in the Tent [as the verse states, And the Eternal appeared in the Tent in a pillar of cloud].