A number of important aspects are of note here. The first is that the Sabbath was not made for its own sake, as with the other days of the week, but with the specific purpose of being a service to mankind. An alternate translation is that it was made "on account of man."
The Sabbath, then, is a specific, thoughtful gift of the Creator to serve His creation. If it were to be used by mankind merely for physical rest, any one of the seven days of the week would be acceptable. Yet, God set apart the seventh day specifically and linked it to creation (Genesis 2:1-3). Therefore, God's purpose in establishing the Sabbath is primarily to support man's part in God's spiritual creation. Such use goes far beyond mere bodily rest.
A second item is that God made the Sabbath for humanity, not just for the Jews. As God created it, its intention is universal. He made it to ensure mankind's physical and spiritual well-being.
A third point is that Jesus claims the authority as its Lord to teach us how to keep it, not whether to keep it. Both the immediate context and the gospels as a whole show that Jesus expected it to be kept and offered no alternatives.
Nations routinely honor citizens they believe have made significant contributions to the well-being of their people, and they often do this by setting apart a day as a memorial to them so that others will remember their contributions. For example, in this nation George Washington, Abraham Lincoln, and Martin Luther King have been so honored. God says in Exodus 31:13: "Surely My Sabbaths you shall keep, for it is a sign between Me and you throughout your generations that you may know that I am the LORD who sanctifies you."
By God's own words, He is memorialized and therefore honored by our observance of the Sabbath (the day we call Saturday). Compared to any man, God's contributions to the well-being of every living thing are beyond counting, but one stands out as witness to all: He is Creator. What an awesome statement to consider. Everything in and on this fantastic, floating greenhouse we call Earth is a tribute to and witnesses of His genius, power, and loving providence.
Mankind, on the other hand, has yet to create its first flea! Yet, if a man did create one, how much publicity would he want? What honors might he demand?