Parashat Pinchas

Ah Gutten Erev Shabbos!

In this week's parsha, the Torah writes about the korbanos that were brought in the Beis HaMikdash every day, on Shabbos, on Rosh Chodesh, and on Yomim Tovim, as it says:

(9) "And on Shabbos, two male lambs in their first year, without blemish, and two tenths of an ephah of fine flour for a meal offering, mixed with oil, and its libation.
(10) This is the burnt offering of every Shabbos, besides the continual burnt offering and its libation.
(11) And on Roshei Chodoshim you shall bring a burnt offering…"

The Question:
Just as we read the korbanos of Rosh Chodesh on Rosh Chodesh, and the korbanos of Yomim Tovim on Yomim Tovim, why do we not read on Shabbos Maftir the parsha of the korbanos of Shabbos? What could be the difference between Shabbos and Rosh Chodesh and Yomim Tovim?

This question is asked by the Rishonim, and from their answers we can learn a few interesting points about why and how Chazal established the minhag of the Maftir reading the way they did.
The Daas Zekeinim MiBaalei HaTosafos asks this question and gives two interesting answers.
1. (This answer is also brought by Tosafos in Megillah 23a.) The purpose of reading the parshiyos of the korbanos is for atonement. Hashem told Avraham Avinu at the Bris Bein HaBesarim that during the time of exile, when we no longer are able to bring korbanos, "If they read before Me the parshiyos of the korbanos, I will consider it as though they brought them before Me."
Therefore, since the purpose of reading these parshiyos is for atonement, we read only those parshiyos where the korbanos are described as bringing atonement, such as the korbanos of Yomim Tovim and Rosh Chodesh. However, regarding the korbanos of Shabbos, atonement is not mentioned, and that is why we do not read that parsha as Maftir on Shabbos.
The Daas Zekeinim MiBaalei HaTosafos writes:

One may ask: Why do we not read every Shabbos this parsha of "And on the Shabbos day…," just as we read on Rosh Chodesh and the festivals their additional offerings?
...We could explain that these parsha readings are for atonement, as we find in Maseches Taanis. When Avraham Avinu asked, "How shall I know that I will inherit it?" meaning, by what merit will I inherit it, Hashem answered him, "Take for Me a three-year-old calf," referring to the korbanos. Avraham replied: That is while the Beis HaMikdash stands, but what will happen when the Beis HaMikdash no longer stands? Hashem answered: They should read before Me the parshiyos of the korbanos, and I will consider it as though they offered them before Me, and I will atone for them.
Therefore, in all the parshiyos of the festivals and Rosh Chodesh, atonement is mentioned, as it says, "One male goat for an atonement for you." But in the parsha of Shabbos, atonement is not mentioned. Therefore, we do not read it.

The Daas Zekeinim MiBaalei HaTosafos gives another answer.
The source for reading the korbanos of Rosh Chodesh and the festivals is learned from the pasuk, "These are the appointed times of Hashem, which you shall proclaim…." Therefore, this Halacha applies specifically to the Yomim Tovim. Shabbos, however, is not called a moed and is therefore not included.
We find that Rosh Chodesh is also called a moed, as it says, "He proclaimed against me a moed to break my young men," referring to Rosh Chodesh Av.
The Daas Zekeinim MiBaalei HaTosafos writes:

Alternatively, regarding the festivals it says, "These are the appointed times of Hashem, which you shall proclaim," and the simple meaning of the verse implies a public Torah reading. But regarding Shabbos this is not written, nor is Shabbos called a moed. Rosh Chodesh, however, is called a moed, as it says, "He proclaimed against me a moed," etc.

Tosafos in Megillah (23a) also asks this question and adds two answers.
Tosafos writes that since the haftorah each Shabbos must be connected to the Maftir reading, if we would read the korbanos of Shabbos every week, we would always have to read a haftorah on that same topic. It would come out that every haftorah throughout the year would discuss the same subject. (This explanation is also quoted in the Mishnah Berurah, Siman 283:1.)
The other answer of Tosafos is discussed by the Rishonim, and it is also brought in the Shulchan Aruch (Orach Chaim 283:1).
Tosafos writes:

The reason we do not take out two Sifrei Torah every Shabbos to read in the second one "And on the Shabbos day," as we do on Yom Tov, is because that parsha contains only two pesukim, and one may not read fewer than three pesukim from the Torah. Nor can one begin from the previous parsha or continue into the next one, because it would not be related to the subject of the day.

This is also brought l'halachah in the Shulchan Aruch (Orach Chaim 283):

"The reason we do not take out a second Sefer Torah on Shabbos to read the parsha of the Musaf korbanos is because it contains only two pesukim."

However, the Daas Zekeinim rejects this explanation and writes, that on Rosh Chodesh we also read the parsha of "U'Veyom HaShabbos," even though it is not related to the subject of the day?
The Daas Zekeinim writes:

One cannot say it is because this parsha has only two pesukim, and the Gemara in Megillah says that one may not begin a parsha with fewer than three pesukim. We could simply begin with the previous parsha, "Command Aharon... My offering, My bread," just as we do on Rosh Chodesh that falls on Shabbos.

B'ezras Hashem Yisborach, I found that the Sfas Emes asks this question (Megillah 23a).
He explains that Tosafos holds that the actual parsha of the korbanos of Shabbos contains only two pesukim. Since that is not enough for an aliyah, it cannot be read on its own, whereas on Rosh Chodesh the actual parsha of the korbanos of Rosh Chodesh contains five pesukim, so it can be read on its own, and additional pesukim may then also be added from a section that is not related to Rosh Chodesh.
The Sfas Emes writes:

However, this can be explained by saying that here (Shabbos) it is different, because the actual parsha of the day contains only two pesukim. Therefore, it is not fit to be read even for one aliyah unless it is combined with another section, unlike Rosh Chodesh, where the actual parsha contains five pesukim, and therefore we can combine it with a section that is not related to the subject of the day.

On behalf of the entire staff of the Sheilot website, we wish you a Shabbos Shalom U'Mevorach.