You don't understand because you're capable of looking at it from just one possible viewpoint.
The process is precisely the important part. And allowing angry mobs (especially those not seeking truth) to dictate the process and hand down vigilante punishments prior to any guilt/innocence verdict, even before any honest collecting of facts, is wrong.
The question in this situation is "Which wrong am I more comfortable accepting?" At this particular junction in time, my first preference is to smack down the angry, destructive mobs and deal with law enforcement issues at later time.
If the mob stood for truth, calmness, and civility, I'd be more inclined to want a trial to take place. But this mob does not stand for any of those. They may claim they are in media statements, but actions most certainly speak louder than prepared statements.