I finally have the answer why the CDN menu option doesn't appear.
The following from Windows Azure Technical support:
"We’re in the process of building out our next generation Windows Azure Content Delivery Network (CDN) architecture, and during this time we are no longer accepting new CDN customers.
With the CDN functionality having recently transitioned to the new Azure management portal, we have enabled it automatically only for customers who were using CDN in the old management portal, so they can continue to manage their CDN configurations. For everyone else, the CDN feature is not enabled in the new portal.
We highly encourage you to wait until we’re ready building our next generation Azure CDN service."