If you are trying to delete a category but the delete option is grayed out and unavailable (1) then this means that this category cannot be deleted. 

This happens because the category is not empty. In the above screenshot, you will notice that the category which has two courses has grayed out the delete operation on it, while the other category which has no courses can be deleted.

So in order to delete a category, you need to remove all courses from that category and leave it empty.