This is more than likely happening because the Event is tied to a registration and/or shared to multiple Categories.

In order to delete the Category, the Events must first be deleted one by one within that Category. 
  1. To delete a event click into the event category and click the red X to remove each event.
If it is a shared event you will get the following pop up box:

Warning: You just hit the Delete button on content that shows up in multiple places.

Event Category X
Event Category Y
Event Category Z

Would you like to remove this content from Event Category X only or truly delete it by removing from all the places it appears? 

Remove from Event Category X only
Remove from all places and delete forever
  1. Click Confirm
  2. Once deleted from that Category you will be able to then delete the Category itself by clicking the red X next to the Category name.