Here's how I see it. He was being an ass back then at the bar and got a beating for it. She taunted the lot of them back there, because they were too pussy to face Makaku, even though it's their goddamn job to do so.
Later on it wasn't her fault that he was a vindicative bitch for getting a minor beating and tried to get her executed by the authorities, because his ego could take it that she was better than him or that she didn't remember his name among the 20 other assholes she beat up that day.
Not her fault that he went insane and killed his girlfriend and then went even further into insanity. If you blame Alita for that, you can also start blaming anime and video games for mass shootings by deranged students.
Finally, she did actually go after him to finish him of, but gave the old man his prey so that he can rest easy. The old man also did finish the job. How is she suposed to know that there's an insane genius out there that can restore human brains from basically nothing? Nova himself said that the brain was basically just goo when his assistant found it.
Sorry, but there's not all that much actual blame to be put on Alita. It was just a really bad chain of events from her (and my) POV.