I'm not sure why exactly, but Facebook likes to keep you from seeing posted YouTube videos in full screen. They do this by adding an allowfullscreen="false" parameter to any embed code that you post. I created a workaround for this via a bookmarklet. If there is a video in your news feed that you want to see in full screen, here's what you can do. First, drag the following link onto your bookmarks toolbar. Chrome users can press ctrl+shift+B to make this toolbar appear. IE users will have to right-click the link and choose "Add to Favorites", then "Favorites Bar".

Full Screen

Next, go to Facebook. Find the YouTube video. Click on the thumbnail image with the blue play button so that the actual video appears. Next, click on the bookmarklet you just created on your bookmarks/favorites toolbar. Finally, press the fullscreen button on the bottom right of the YouTube video. Voila, it now works!

P.S. -- This bookmarklet should allow you to fullscreen any video (not just YouTube) posted to any site (not just Facebook), provided the video has a fullscreen button within the player.