It says in Vayikra(16:30) Lefnei Hashem Titaharu. The mishna in keilim(17:14) says certain days of creation the items of that day can become tamei.On Sunday earth was created and earthenware can become tamei.On Tuesday trees were created which can become tamei.On Friday animals and man were created which can become tamei.On Monday, Wednesday, Thursday are all days that the items created cannot become tamei.
The Calendar used today, yom kippur can only fall out on mon,wed,thurs,and Shabbos.It makes sense for the the holiest day of the year to fall out on the purest days.(Avnei Shoham/shabbos delights)