I'm amazed at people that get on twitter and say horrible things to other people they don't even know.
Amazed? I can see "disappointed" or "saddened", but we have a vast corpus of evidence from the past few decades demonstrating that sort of behavior is normal in online discourse. I have academic articles discussing it from the mid-1990s, and it was a truism among regulars on Usenet and BBSes and other online forums as far back as at least the early '80s.
It seems that a few factors in particular compound to increase the probability of adversarial communication with strangers online: a low barrier to entry (it takes very little time or money to dash off an angry reply), immediacy (most of these channels are low-latency so there's little "cooling-off" time), narrow feedback (you can't see the person you're arguing with or hear their tone of voice), and a lack of corrective sanctions from the community.
These add up to making the cost of flaming very low, and the psychological reward high. The latter is due to that immediacy plus the evolved inclination to win arguments, as demonstrated extensively by any number of (relatively) sound psychological experiments over the past century.
Arguing rationally is learned behavior and requires an investment mindset - you give up the short-term reward in favor of longer-term ones such as self-actualization ("I am the sort of person who resists the urge to flame and wins arguments on merit") and possibly more-durable reputation in certain social circles. It means doing work in online discussions, and most people treat those as entertainment and want to avoid the additional labor.
So points for you, and it's something we all ought to aspire to; but as long as people are the sort of people we'd recognize, it's going to be a minority behavior.
 Hell, I wrote one that touches on it myself, in the "Geographies of Cyberspace" special issue of good ol' Works and Days.