Welcome to the wonderful world of copy protection.
Apple's Mac lines includes a form of digital copy protection that will prevent protected media, such as DRM-infused iTunes movies, from playing back on devices that aren't compliant with the new priority protection measures.
The Intel-developed technology is called High-bandwidth Digital Content Protection (HDCP) and aims to prevent copying of digital audio and video content as it travels across a variety of display connectors, even if such copying is not in violation of fair use laws.
Among the connectors supported by the technology are the Mini DisplayPort found on Macs, in addition to others such as Digital Visual Interface (DVI), High-Definition Multimedia Interface (HDMI), Gigabit Video Interface (GVIF), Unified Display Interface (UDI) and Thunderbolt.
Apple has apparently acquired a license for the technology and is now using it across its lines to to prevent transmission of purchased iTunes content (and some DVDs) to devices that don't include support for HDCP.
The problem can often be solved by using an HDMI to Component Video adapter. Component Video will give you a better HD picture than HDMI without any of the hassles of HDCP.
Generally try to avoid using HDMI. When able, use Component Video. With Component Video you get full HD quality and you will never have HDCP hassles (which of course is why Hollywood wants to ban it).