Reasons
The modern Hebrew calendar has been arranged so that Yom Kippur does not fall on a Friday or Sunday, and Hoshana Rabbah does not fall on Shabbat. These rules have been instituted because Shabbat restrictions also apply to Yom Kippur, and if Yom Kippur were to fall on Friday, it would not be possible to make necessary preparations for Shabbat, including candle lighting, because the preceding day is Yom Kippur. Similarly, if Yom Kippur fell on a Sunday, it would not be possible to make the necessary preparations for Yom Kippur, including candle lighting, because the preceding day is Shabbat. Also, the laws of Shabbat override those of Hoshana Rabbah, so that if Hoshana Rabbah were to fall on Shabbat certain rituals that are a part of Hoshana Rabbah services (such as carrying willows, which is work) could not be performed in that year.
As a consequence, in the case of Yom Kippur, which falls on 10 Tishrei and cannot fall on a Friday or Sunday, the days in Cheshvan and/or Kislev are adjusted so that Rosh Hashanah, which falls on 1 Tishrei, does not fall on a Wednesday or Friday. And, in the case of Hoshana Rabbah, which falls on 21 Tishrei and cannot fall on a Saturday, Rosh Hashanah cannot be on a Sunday. This leaves only four days on which Rosh Hashanah is allowed to fall: Monday, Tuesday, Thursday and Saturday, which are also referred as the "four gates".
Read more about this topic: Days Of Week On Hebrew Calendar
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