It comes down to conflicting religions for using the bible as source materals. The original authors of the bible were Jewish, a celebrate the 7th day of creation from biblical book of Genesis on the day currently called Saturday. From this interpretation, Saturday is in fact the last day of the week, as it is the 7th day, and the day of rest and worship.
Unfortunately, Christianity shifted their day of worship to the day of the week where Christ was raised from the dead (or more to the point, discovered to have been raised from the dead). For Christ and his followers were Jewish, and he was crucified on a Friday and hastily burried (the day of rest officially begins at sunset on Friday, and according to Catholic tradition, Christ died at ~3pm, and was hastily burried before sunset). No one could go to the tomb on Saturday since it was their day of rest, and the first oppertunity to provide a proper internment was Sunday, when they found the tomb open and the body missing.
So now that you had your little religious lessons, Christinanity changed the day of worship to Sunday, the day of Christ's rebirth, thus leading to the inconsistencies in what day of the week is the actual week end, Saturday or Sunday, as for thousands of years before Christinanity for all the people who ascribed to the 7 day week, Saturday was the last day of the week. Christianity celebrating a rebirth and renewal really shouldn't change that message, as thus worshiping the "beginning" as opposed to the "end" would seem to fit their message better and was probably one of the original reasonings for the shift.
Similarly, Islam, which is also based in part by the books in the bible (particularly Genesis), decided to use Friday as opposed to Saturday or Sunday to also distinguish themselves as different from the Jewish and Christian traditions.
However, the calendar we use that you are discussing is the Julian calendar, based on the Roman system which became Christian system when the Roman Emperor converted and mandated the change. This then leads to some of the deliema as to the end of the week, as the Roman's were using a 7 day week, and aligning the last day of the week, the 7th, with Sunday (obviously previously the day celebrating the Sun, and often the main day of worship in the pre-Christian religions across the Roman Empire).
So to make a long story short, blame religions and the conflict between the Book of Genesis and the newer religions for when the week ends, Saturday or Sunday....