'User Account' menu link does not show to anonymous users
That is a feature. An anonymous user doesn't have an account nor can he log out, why should there be links to these pages?

You might want to update your question to better explain what you actually want instead of explaining how it works right now :)

EDIT: To have a link to the Login page, just create a menu entry that points to /user/login. Just like /user/logout, this link will only be shown if you can log in (which means that you are not already logged in).