Can't insert cells in Excel 2010 - "operation not allowed" error message

As the message indicates, you're trying to insert rows into a Table in your sheet. Typically, but not necessarily, tables will have banded formatting. When you click in a cell in a table, the Table tab will appear, like so:

The Insert and Delete commands get grayed out when there's more than one table intersecting the row you're trying to delete (and maybe other times):

I haven't figured out how to "Insert Copied Cells" into just a table row in one step. Instead I insert a row, or rows, into the table and then copy the content. To insert a row into the table, right-click a cell in the table and choose Insert:

You can turn the tables back into normal cells. Do it like this:

I am not sure if it was the same problem, but I had a similar issue on a large spreadsheet where I had many rows and columns hidden. I would try to add or delete rows or columns and got a message similar to what you had. In many cells I had comments, I discovered that although the comments were linked to a specific cell, you could move them and they could be anyplace on the spreadsheet. If you tried to hide, delete, or insert rows/columns that had those hidden comments you got an error message that would go off the table. I made all the comments visible, and then moved them to a spot I was not trying to affect and no more problem.

I was getting the same error. "This operation is not allowed. The operation is attempting to shift cells in a table on your worksheet."

Tried the suggestions, but everything looked correct. Ended up just converting all 4 Tables to Range and then back to Table. Don't know which Table was the problem, but it's all good now. ;)

Thanks!