> The end of the end of the week cannot be the beginning of the week.
Of course it can. The word “weekend” just refers to the block of free time starting at the end of the working week. It doesn’t have any direct relation to the way weekdays are laid out on a calendar. The word was invented in England at a time when the English still considered Sunday the first day of the week, a hundred years before ISO 8601 moved Monday to the start for commercial reasons (as described in Annex A).
When a public holiday falls on Monday, my friends and I call that weekend a “three‐day weekend” or a “long weekend,” even though the Monday falls well within what a strict ISO 8601er would consider the next week. What makes the weekend the weekend is when the weekend starts—the end of the work week—not when the weekend ends.
Dictionary.com, Merriam-Webster, and Cambridge all define the weekend as some derivation of "the end of the week".
I'm also not sure how the various definitions and historical context has anything to do with the claim that the end cannot be the beginning. If the end were the beginning that particular day would belong to two different weeks, but that's nonsense. The last day of the prior week and the first day of the current week are two different days, therefore:
> The end of the end of the week cannot be the beginning of the week.
The weekend has always been innately tied to the work week specifically, both historically and in current usage.
> Dictionary.com
Has as the third listed definition: “any two-day period taken or given regularly as a weekly rest period from one's work.” And has a whole paragraph describing usage, including: “More strictly speaking, the weekend is thought to consist of Saturday and Sunday (often regardless of whether the calendar week is considered to begin on Sunday or Monday). In practical terms, the weekend is typically considered to be the period between the end of the workweek (or school week) and the beginning of a new one—which is why most people consider their weekend to start on Friday night, after work or school.”
> Merriam-Webster
“the end of the week; the period between the close of one work or school week and the start of the next”
> Cambridge
“Saturday and Sunday, or Friday evening until Sunday night; the part of the week in which many people living in the West do not go to work”
Every dictionary you cited agrees that the weekend is or can be defined in relation to the work week!
> If the end were the beginning that particular day would belong to two different weeks, but that's nonsense.
Millions of people living in cultures where Sunday is the first day of the week have no problem with the concept of a single weekend consisting of a Saturday from one week and a Sunday from the next. There’s no logical contradiction. “Monday as the beginning of the week is the only logically defensible position if you support the weekend” is a false statement, because a single weekend is not required to consist solely of days from the same week.
There is only one weekend. One end of the week. It goes at the end as it is definitionally required to do.
If Sunday is the end of the weekend, it is the end of the end of the week.
The end of the end of the week cannot be the beginning of the week.
Sunday comes after Saturday comes after Friday...comes after Monday.
Therefore, Monday is the beginning of the week.
QED