You must be logged in under the exact same username account that registered a blog to delete it.
To prevent accidental or inadvertent deletion of blogs, there are multiple warnings given that blog deletion is permanent. If you delete a blog you will not be able to get it back and no one else will be able to use that blog address. You must be sure you never want to use the blog again if you delete it. Lastly, a verification link is sent in an email and must be clicked to delete a blog. http://en.support.wordpress.com/delete-site/