By Rav Avrohom Dovid Waxman
The Rema in Hilchos Pesach (Orach Chaim Siman 490:9) brings the minhag to read the Megillah of Shir Hashirim on Shabbos Chol Hamoed Pesach, Koheles on Shabbos Chol Hamoed Sukkos, and Megillas Rus on Shavuos. The Magen Avrohom explains the reason for each: Shir Hashirim includes pesukim about Yetzias Mitzrayim, Sukkos is Zman Simchaseinu and Koheles speaks about proper simcha, and  quoting the Medrash Yalkut Rus, we read Rus during Zman Matan Toraseinu to teach us the derech to receive Torah includes suffering and Yisurim. The Machzor Vitri (Ois 312) and Rokeach (Shavuos, Ois 296), specify to read Rus before Krias Hatorah, as is our custom.
The Achronim ask, how do we lein Rus before Krias Hatorah? The klal is “Tadir V’sheino Tadir, Tadir Kodem (Zevachim 89a ),” when there are two mitzvos to be performed, the mitzvah which is more common takes precedence, and is to be performed first; Rus is only on Shavuos, while Krias Hatorah is far more often?  The same may be asked of Koheles on Sukkos and Shir Hashirim on Pesach. Why do we lein them before Krias Hatorah, when Krias Hatorah is a more common mitzvah?
The Sha’agas Aryeh (Siman 22) explains that the rule of “Tadir V’sheino Tadir, Tadir Kodem” only applies when the two chiyuvim to be performed are similar, either both Mideoraysa or both Midrabanan. If, however, one mitzvah is Min Hatorah and one is Midrabanan, the Midrabanan is like a dvar reshus compared to a Deoraysa, and would not be subject to the klal of tadir kodem. Just as one may do a dvar reshus, a non-mitzvah, before a mitzvah, a Drabanan is like a dvar reshus in relation to  a chiyuv Mideoraysa. Based on this, we can explain that since Krias Hatorah is Drabanan, and Kriyas Rus is only a minhag, a minhag is considered a dvar reshus in relation to a chiyuv and “Tadir V’sheino Tadir, Tadir Kodem” does not apply.  (Even according to the Tzla”ch Brochos 51a, that argues with the Shaagas Aryeh and says a Deoraysa must come before a Drabanan, would agree that a minhag in relation to a drabanan is a dvar reshus and “Tadir V’sheino Tadir, Tadir Kodem” does not apply.)
What still requires further explanation is, why is  the minhag is to read the megillos specifically before Krias Hatorah?  If there is no din tadir kodem, there should be no preference on the order? The Tiferes Bonim answers in the name of Hagaon Harav Elyashiv Zatza”l , is that we specifically lein Rus before Krias Hatorah to avoid the possible error that Rus is a second Haftorah, as it would appear were  it to immediately follow the first Haftorah. On Purim, since there is no haftorah, the megillah follows Krias Hatorah.
Let us suggest another answer:  The halachah is that on Shabbos Rosh Chodesh, first the Parshas Hashavua is read, followed by the kriah of Rosh Chodesh. The Turei Even (Megillah 29b) asks, the reading of that particular parsha only occurs once a year, while the Rosh Chodesh kriah is read each month, so why is the kriah of Rosh Chodesh not first, based on the rule “Tadir V’sheino Tadir, Tadir Kodem?” The Turei Even answers that all the readings of the parshiyos on Shabbos fall under one category, called Krias Parshios Hatorah, and therefore is more tadir since it occurs weekly, in comparison to Rosh Chodesh kriah, which is a monthly occurrence. This requires further explanation: why does the Turei Even consider the parshas hashavua readings one all-inclusive obligation, while Rosh Chodesh is a separate obligation that only occurs on Rosh Chodesh? Is it not all one takanas chachamim to have krias hatorah, with designated times for each part of the Torah different times of the year?
The answer lies in the source and cause of the takanah for each of the kriahs. Chazal were mesaken the kriah of Parshas Hashavua so that people should not go three days without Torah, as found on Baba Kama 82a. In other words, the kriah is in order to have a fulfillment of mitzvas Talmud torah btzibur, which is accomplished throughout the year by reading portions of the Torah and completing it annually. The kriah of Rosh Chodesh, however, is actually an obligation of Rosh Chodesh, as the the gemara Megilla 31a says, the posuk “Vayidaber Moshe es Moedei Hashem el Bnei Yisroel” teaches us that on each Yom Tov, we must read the relevant part of the Torah to that Yom Tov. Rashi explains that this posuk is the source for reading the kriah of Rosh Chodesh on its designated time, as well. The kriah of the Parshas Hashavua and the kriah of Rosh Chodesh are clearly two different takanos. That is why the Turei Even considers all the parshiyos hashavua as one category, which occurs “tadir”, enacted for the sake of not being mevatel talmud Torah for three days. Krias Rosh Chodesh, on the other hand, is an obligation of the day of Rosh Chodesh, and is only a monthly chiyuv, and less “tadir”, so it is leined second.
A proof can be found to this yesod: The Tur (Orach Chaim 676) discusses the halachah of which kriah to lein when there is a ta’anis tzibur on a Monday or Thursday. The Sar Shalom holds that the kriah of the Ta’anis Tzibur, “Vayichal,” must be read. Others say  to lein the kriah of the parshas hashavua, as we do on all Mondays and Thursdays, because it is more tadir than the kriah of a ta’anis tzibur. The question is, why does the Tur consider Parshas Hashavua more tadir? The kriah of the parsha happens only once a year, while the kriah of Vayichal is a chiyuv on every ta’anis, many more times than the Monday and Thursday of the Parshas Hashavua? We see from the Tur that since all the Parshiyos Hashavua are part of the chiyuv to learn Torah, and as we explained in the Turei Even, all part of one chiyuv that is every Shabbos, it is far more tadir than Vayichal which is a chiyuv of a Ta’anis and is only a few times a year.
We can apply this principle to our question, of Megillas Rus, as well. The kriah of Shavuos, like the kriah of Rosh Chodesh, is an obligation of the day being the Yom Tov of Shavuos which requires kriah b’zmano. Each Yom Tov has its own, unique obligation to have a kriah. Krias Shavuos, is therefore a once a year obligation, and obviously not more  tadir than the leining of Rus which also occurs annually.
However, that makes them both chiyuvim that happen once a year, so why does the Machzor Vitri and Rokeach say to lein Rus specifically first, if they are equally tadir? The answer is, if we look at the source of the kriah of Megillas Rus, it is apparent that Rus is indeed more tadir. From the Magen Avrohom mentioned earlier, that includes all three megillos together with their reasonings, it would  appear that the minhag  to lein Rus, Shir Hashirim, and Megillas Esther, are in reality part of one minhag, established in order to lein all the  megillos throughout the year. The minhag was established to lein the megillos bdavka on each of the the Yomim Tovim, because the Magen Avrohom explains that each have a reason that makes it relevant to the Yom Tov. As so, Megillah leining, which occurs on all Shalosh Regalim, is more tadir than than the kriah of Shavuos, which is a chiyuv of the Yom Tov and is only once a year. According to this understanding, Rus is in fact more Tadir than the kriah of Shavuos, since the megillos of Shir Hashirim, Rus, and Koheles, are one category and mechayev.
Megillas Esther on Purim and Megillas Eichah on Tisha B’av, however, are not in this category and are chiyuvim of the day. Megillas Esther is a requirement of the Yom Tov of Purim, and Megillas Eichah is a requirement of Tisha B’av. Since they are kriyos that are chovas hayom, we can now explain why on Purim and Tisha B‘av, the Megillos are read after Krias Hatorah. Kriahs Hatorah of Purim and Tisha B’av are a chovas hayom and  Eichah and Esther are chovas hayom, making them equally tadir.
The  question that remains, concerns why we read Shir Hashirim and Koheles before Krias Hatorah. We explained Rus, which is read on Yom Tov, to be more tadir than the Yom Tov kriah. But Shir Hashirim and Koheles are read on Shabbos Chol Hamoed, and Shabbos is a  weekly kriah, so the rule  Tadir Vsheino Tadir, Tadir Kodem should apply to require Krias Hatorah first?
We would like to suggest, that although the kriah of Shabbos Chol Hamoed is a fulfillment of the takanah not to be mevatel Talmud Torah like other Shabbos Kriyos, and is therefore consisting of seven aliyos like all Shabbos Kriyohs, the kriah of Shabbos Chol Hamoed is different in its mechayev. Rashi in Megillah 31a explains that the kriah of Shabbos Chol Hamoed is very relevant to the day, including mention of the Yom Tov, Chol Hamoed, and Shabbos. Therefore, the mechayev of Kriyas Shabbos Chol Hamoed is also a chovas hayom, a unique obligation of the Chol Hamoed of that particular Yom Tov. As a chovas hayom, it is an obligation that that occurs once a year and less tadir than Shir Hashirim and Koheles, which are part of the category of Krias Hamegillos that occurs three times a year. So in fact, reading the Megillos of Shir Hashirim and Koheles first are also a fulfillment of Tadir V’sheino Tadir, Tadir Kodem.
Adapted from the Kuntres Yoma D’Atzarta on Shavuos written by Harav Avrohom Dovid Waxman Shlit”a, R”M B’Yeshivas Mishkan Hatorah, Lakewood
{Matzav.com}