Steven Sinofsky has published
an article which explains why Internet Explorer 10 for Windows 8 will not be supported by Adobe Flash.

The new IE will run by default
in plug-in free mode , in which plug-ins (including a plug-in for displaying Flash) and embedded ActiveX components are not available.
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The problem of plug-ins in high power consumption, which is unacceptable on laptops and smartphones. In addition, plug-ins often threaten security and reliability, and their interface does not match the
Metro style that Microsoft promotes.
On the other hand, HTML5 allows you to do almost everything for which Flash and ActiveX were previously used. Many large portals (for example,
YouTube ) already provide versions of their sites rewritten in HTML5 and not using Flash.
For backward compatibility, IE10 provides for switching to Use Desktop View mode, where the Flash plug-in will be available.
In general, the article describes about the same reasons as in the famous
letter of Steve Jobs about the refusal to support Flash on iPhones.