How could someone get so personally affected by this story that they're willing to kill someone and put their own life in danger as well?
Because think about what was involved in this case: Caylee Anthony was two and a half years old when she died. Her disappearance was not reported for a month. Her mother was spotted partying just hours after her death, and the prosecution argued that Casey Anthony killed her daughter so that she could start a new life with her new boyfriend, and she repeatedly lied to police during the investigation. The prosecution went in for charges of first-degree (premeditated) murder, aggravated child abuse, and aggravated manslaughter. All of them are serious charges; first-degree murder carries the death penalty in Florida. So at the worst, Casey Anthony was a callous child killer; at best, she was a negligent parent. That can really whip people up into a frenzy - just look at the Kiesha Abrahams case here in Australia, which is remarkable similar: when her mother and step-father were first brought into court, there was already an angry mob outside the courthouse. The difference in the Caylee Anthony case was that it got picked up by social media. It got massive media coverage all over the world, though a lot of it was brawls between people trying to get into the courtroom for the verdict. The big problem in this case is that the public had already judged Casey Anthony guilty before the trial was over. They were
expecting a guilty verdict, but they had not heard all of the evidence - and what evidence they did hear was diluted by pundits analysing it and grandstanding to audiences because they knew it would get ratings.
Running someone off the road out of anger is pretty serious. It's really hard to do that without the intention of killing them. I'd say that trying to kill someone out of personal anger, without even knowing the person you're attacking is the person you're angry at, is quite a serious issue, which requires a relatively large amount of mental instability to commit. Compared to say, getting mad and beating up a guy because he's harassing a girl. That's not necessarily the right action either, but it's a very different scenario.
Remember, the attacker wasn't trying to kill the woman she ran into - she was trying to kill Casey Anthony. She believed that Anthony was guilty of being a child killer, and that in killing "Anthony", she was doing the right thing. I've seen pictures of Casey Anthony and "Casey Anthony", and they do look similar.
Anger is a powerful motivation. A lot of murders happen because one person is incredibly angry at their victim - like say, someone who kills a man because that man is sleeping with his wife. I'm not trying to justify what the woman did when she ran the Anthony look-alike off the road; I'm just saying that intense anger is not a mental illness. The Anthony case has gotten massive media attention (it was even getting a lot of coverage here in Australia in the days before the verdict), so it's not like the attacker just ran the first person she saw off the road. She had clearly been following the Anthony case and decided she was guilty, and when she saw who she believed to be Casey Anthony, she ran the other woman off the road with the intention of killing her because of it.