For on this day (Yom Kippur) Hashem will forgive you to purify you etc. (16:30)
The day of Yom Kippur is the holiest day of the year. R’ Yitzchok of Koritz points out an amazing fact regarding the days that Yom Kippur can or cannot fall out on that serves to demonstrate just how deep the holiness of Yom Kippur runs.
The Mishna (Keilim 17:14) goes through the 6 days of creation and differentiates between what was created on each day and makes 2 categories, days that had things that could conduct impurity created on them and days that did not have things that could conduct impurity created on them.
Day 1 had things created on it that can conduct impurity. R’ Ovadia MiBartenura explains that the earth was created on the first day and if one forms vessels out of the earth – earthenware utensils, they are susceptible to becoming impure. Day 2 the heavens were created which do not conduct any form of impurity. Day 3 saw the creation of trees, which, should utensils be made out of them, they could conduct impurity. On day 4 and day 5 the birds and fish were created which from the Torah, even if utensils were to fashioned out of their bodies, they would not conduct impurity. MD’Rabbanan however, they do (this will be significant later). Everything that was created on day 6 is susceptible and conducts impurity, animals, vermin, and humans. All of them, should utensils be made out of their bones or skins - they can be rendered impure.
Thus, in summation, on days 2, 4, 5 and Shabbos nothing being able to become impure was created while on days 1, 3, and 6 the items and beings created can at some point be conductors of impurity.
After learning this mishna, it is by no coincidence that the days of the week that Yom Kippur, the holiest day of the year on which we are purified, can fall out on. Amazingly, Yom Kippur can only fall out on Monday (2), Wednesday (4), Thursday (5) or Shabbos, the very days that no things that can conduct impurity were created. As well, it never can fall out on Sunday (1), Tuesday (3), or Friday (6), the days that conductors for impurity were created.
The Yehudi Hakadosh takes this idea a step further. Purim, which the Zohar compares to Yom Kip’purim (that the holiness of Purim is likened to Yom Kippur) can only fall out on the days that conductors of impurity were created. The days are Sunday (1), Tuesday (3), or Friday (6). (Wednesday and Thursday will be addressed shortly.) Yom Kippur was originally singled out as a day of total purity and since its inception, was destined to be the holiest day of the year. Whereas the day of Purim originally was destined to be a day of massacre to the Jews and only later became a holiday. Therefore, it falls out only on the days the things that can conduct impurity were created on and by us celebrating it as a holiday, this purifies the day.
On Wednesday (4) and Thursday (5), both Yom Kippur and Purim can fall out on. This is because Min HaTorah the creatures that were created on these days don’t conduct impurity, therefore, Yom Kippur can fall out on these days. However, the Rabbanan decreed that some of the creatures created on days 4 and 5, should utensils be made from them, they can conduct impurity. As a result, although Purim only falls out on days that conductors of impurity were created, since Purim is a holiday MD’Rabbanan and these creatures can conduct impurities MD’Rabbanan, Purim can also fall out on Wednesday and Thursday and so can Yom Kippur.
Based on this, R’ Menachem Zemba answers a question that is asked by many on the Mishna in Keilim mentioned earlier. At first glance, the Mishna seems to have no halachic ramifications since what difference does it make if on days 2,4,5, and Shabbos nothing that could conduct impurity was created and that on days 1,3, and 6 things that could conduct impurity were created?
However according to what R’ Yitzchak of Koritz said, this mishna does have halachic ramifications. Since the Beis Din that determined when to inaugurate the new Jewish lunar month would have to take into consideration that Yom Kippur should not fall out on any of the day that things that could conduct impurity were created on (see Tosafos Pesachim 58b).