|In a previous post someone indicated they had the same problem - I found a work around when it happened to me so I am posting the answer.|
This happened to me and I resolved it by turning off track changes and changing the workbook so it was no longer shared (it was not password protected). The delete selection was no longer greyed out then. Saved me quite a bit of time because I did not want to have to copy everything to a new workbook.
Evidently when you have track changes on it frowns on deleting entire worksheets - it probably has no way to track this change so it is not allowed.