Twitter is an amazing concept. I've experienced it firsthand since I have my own twitter account as do many of my friends. Previously, other social media accounts don't have the same charm or aspect as Twitter. With Facebook, posts aren't as often and so each post is more important and hold more weight in them. However, twitter goes by so quickly. It's simple and easy to use and since everything goes so quickly, people feel as if their words don't hold as much weight. But if you isolate each post on it's own, the words seem to be a lot deeper than what it was written with.
Twitter's a lot more anonymous than Facebook. Just in general, social media sites are getting more and more anonymous. Twitter only needed an email and a password. In Facebook, many people need to have an actual name, filled in biography, sometimes multiple emails, where they work and more. Twitter became a platform
that more celebrities used because it was easier to keep private things private and only sow one side. Because of this fact, it also gets a lot easier to create multiple accounts- heck on the twitter app you can switch between different accounts with ease and without logging out! This makes people often have multiple accounts for different purposes, rather than a Facebook. A lot of the people I know have anonymous fan account where they express their love for a band more openly, but also another account for posts and tweets that don't pertain to their band. Just as easy it is to maintain a fan twitter account it is to maintain a hate account.
Even if you slip up once or twice and expose private information in your life on twitter, it is easily covered by other tweets. In Facebook, you can just to go their biography page and see what you can see right there.
Regarding anonymous (or even not anonymous) hate, I don't think it's going anywhere. I don't even think it's a super big problem, because people are still expressing feeling that do exist, it's just that they are able to express it more openly whereas before it would be more buried down. If the media deals with it properly and treats hate posts on twitter like actual feelings rather than just mean comments, people will realize the weight of their words more than brushing off mean comments like they do on Jimmy Fallon. The way celebrities deal with hate comments on Jimmy Fallon, to me, only spurs on the hate, because we can see with our two eyes that it doesn't impact them, so we can continue.