why can't i watch this .avi file on my mac (mountain lion)?
OS X doesn't have codecs for AVI files built-in, so you'll either need a plugin to allow QuickTime to play the files directly, or use a different media player that can handle those file types.

For plugins, Perian has been the go to choice. However it is no longer supported or developed — at the moment it still works well, but as OS X changes, that may no longer be the case.

For third party players, VLC is pretty robust and will play virtually anything you can find. It has the benefit of ongoing development, but the interface is not always the best (the preferences in particular are pretty convoluted). You can also look at MplayerX. There are other options (Movist and Niceplayer come to mind), but none seem to have been updated in the past year or more.