You can only delete a breed when there are no more animals of that breed in the administration. If you click on the tab of the breed in the list, you will see exactly which animals are still present in the database. They must all be be removed before you can delete the Breed.
You can remove the breed as follows:
1. Click the menu Management
2. Click the tab Base tables
3. Click the drop down box that says Contact categories and select Breeds
4. Click on the red x in the row of the breed you want to delete.