Twitter is built for harassing. The medium makes it inevitable. you make a tweet and you shoot it out into the ether. It ends up on a couple million twitter feeds whether they asked for it or not. It angers some of those people, and they retweet it to show their followers how stupid you are. Now all their like-minded friends see that tweet in their feeds. A bunch of them are now aware of your existence and are mad and tweet back at you. This is far worse when you participate in a contentious issue on a hashtag. This is before you even get into hate-following and active-deliberate harassers. Then there is scale. There are a couple hundred million people on Twitter. If even .01% of them are sociopaths, that is a near-unmanageable problem.

Finally, a significant portion of Twitter is quite literally trolls trolling trolls. They both can dish it out and take it and don't see the problem. Good for them, but it's not compatible with everybody else.