CUPS is administered via a web page, http://localhost:631/admin/ . This web page requires authentication to access, but elinks fails to open it because it doesn't even prompt for user name and password. lynx, however, does handle password authentication.
{e,}links doesn't support HTTP authentication, and we don't have the resources to add this ourselves. This will have to wait until the base maintainers decide to implement it. Until then, use lynx.