It didn't use to be like this. Users of the Internet used to be largely academics who had access to the service at work, and hobbyists who would occasionally connect on expensive and slow modems from home. Things were slower, and the internet was much more like thousands of islands as against a huge continent. You could connect to mailing lists, or a channel on IRC (Internet Relay Chat) and you might deal with dozens of others, perhaps even hundreds. Such discourse could be easily moderated if needed, to keep things calm.
Twitter is about as different from that as it's possible to be. It a single chatroom, always on and with millions of users. If you get even slightly well-known you can have thousands of regular readers of your comments, and all it takes is a fraction of a percent of those readers to be unpleasant or nasty and you end up with a bad experience. Twitter's design was always going to fail this way. The problem is with the reaction that takes the actions of a fraction of a percent as being representative of millions of others, when it just isn't. Journalists rarely understand statistical sampling, and for them Twitter is a gold-mine of controversy, as self-selecting idiots and cowards are there for all to see.
Yes, some people are vicious and even criminal. That should be dealt with. But it's hopelessly naive to think that Twitter is going to be a pleasant experience for all.