I don't think Twitter is a bad thing, but I do think people tend to screw up a bit due to the immediacy of it. Heck, I've written posts on this various forum, sat there for a second, and completely erased what I wrote. I'll usually do that because the post feels too aggressive, and in reality, I'd prefer to try to take a more neutral tone... even if the post that I'm responding to doesn't. Although, I always thought that was more or less something that younger individuals fought with as they tend to lack the critical thinking to not take things too emotionally. Along those lines, I remember when I was a lot younger, and I "emotionally quit" a forum (i.e. made sure to post about it) due to a debacle. It's that sort of thing that you'd expect a 13-year old to do (as everything is a big deal to you at that age) and not a grown person.
Now, I think my blathering ties into this example of a Twitter snafu, but I think it's also safe to add that some people seem to assume that others are malicious in their actions. For example, you could assume that the lady thought that the guy's remark was some blatant attack on her home life. Well, to be honest, it probably was to a degree, but I think it's better to refer to it as "pointing out the absurdity". Her problem isn't that she disagreed with him, but rather that instead of arguing against him, she took to repeated ad hominem attacks.
In short, if you feel like you're writing some angry tweet, before you hit that post button, relax for a second... or just outright hit the cancel button and put your damn phone down.