It is a security reason. Imagine you have your computer not lock and someone goes on that page. At least, the person won't have his/her account deleted. It's all fine because it's not an operation that is done repeatedly.
For a "Show HN" I'd have expected a blog post/detailed status update/something explaining what changed.
You still have to enter your password to confirm deletion of your account, so there would be no security risk in displaying that info page.
You want to delete someone's account without logging in?
I'd like to see the details without logging in, yes.