לרפואת א"מ ר' יצחק יונה בן חנה ור' מרדכי דוד בן קריינא בתוך שח"י
The Medrash says that every day of the week has a partner. Sunday-Monday, Tuesday-Wendesday, Thursday-Friday. But what about Shabbos? Shabbos "complained" to Hashem that she has no partner. So Hashem said that the Jewish people will be your partner.
The explanation is as follows: We rest on Shabbos as Hashem "rested" when He created the world [Shmos 31-17]. However, the type of work we rest from is dissimilar to the work Hashem rested from. Hashem rested from any creative work. We rest from the labor performed in order to build the Mishkan. So what is the connection?
The explanation is that the creation of Shabbos was the creation of the pleasures of the next world where we will be rewarded for our mitzvos. In contrast, the creation of the six days to to create a space for the Avoda of fulfilling these mitzvos - a מקום עבודה. So that is Shabbos - the creation of the space for receiving reward after the 6 days of creating a space for the Avoda performed in order to receive that reward.
That is where the building of the Mishkan comes in. The formation of the Mishkan was ALSO the creation of a space of Avoda for the Jewish people - just like the 6 days of creation. So essentially - we rest on Shabbos in a similar way to how Hashem rested on Shabbos - from creating a מקום עבודה!!
So it is impossible for the nations of the world to have Shabbos b/c they don't have a concept of creating a מקום עבודה. That is why Shabbos is OUR partner and no one else's. They lack Shabbos b/c they lack the experience of creating a מקום עבודה and then resting from it - as we do. The point is that since the six days of the nations of the world are not similar to Hashem's six days of creation - automatically they cannot have Shabbos.
[עפ"י תורת מרן ראש הישיבה זצ"ל]