H.264 is a standard created by ISO (International Standards Organisation) MPEG and ITU (International Telecommunications Union). It was created by experts from various companies. Every aspect of it is documented although the specification is not free. Every feature is backed up by experiments and scientific proof that it adds value.

WebM is not a standard. It was created by one company who sold the patents and source to Google who have now tweaked it and released it as free. This does not make it a standard.

By dropping the support for H.264 from Chrome, Google is limiting our choice of formats we should use for video. But they still support Flash video which is H.264 in a Flash container so it's not that supporting H.264 is a problem...

Unless someone can show evidence that WebM provides higher quality for lower bit rate or easier coding/decoding then this is just politicking/marketing. Actually, by "dropping support for H.264" but still supporting Flash video then it's a completely null argument because H.264 in it's own container would be more efficient.

By the way, I was looking at adding support for Matroska to my own software but the overhead looks huge and the only place I could find that used Matroska was torrents; not good for commercial software.