shakeyourcaboose I always felt that the strong physical resemblance between Bellatrix and Andromeda was intentional on Rowling's part - that they were probably very similar and very close in their youth, but due to circumstances took very different paths in life. I always felt that either girl could have gone either way.
I saw Bellatrix as a perfect storm, all the elements came together to create the woman she became, but it wouldn't have taken much to send her in a different direction.
I saw Bellatrix as someone who was very loyal and obsessive and desperate to please, and greatly felt the weight of family expectation. She was the eldest, she was expected to be the perfect Black daughter, the perfect pureblood witch. But she was also extraordinary; incredibly clever, incredibly talented (She was able to fight off Dumbledore in Order of the Phoenix), and she was afraid. Afraid that she couldn't live the life she was expected to. This brilliant mind was expected to marry and submit to her husband, produce a pureblood heir. Do basically nothing else. Waste all that potential.
She loved her sisters. And she was someone who loved very deeply. She was devoted to them (see Half Blood Prince.
The one person Bellatrix was willing to betray Voldemort for was Narcissa; she taught Draco occlumency to protect him from her master). When Andromeda left, Bellatrix saw it as a betrayal. Her sister had abandoned her family. That's why she was so angry. That's what she couldn't forgive. And partly, because Andromeda had had the strength to do what Bellatrix had not - she had chosen love over duty and loyalty.
Because Bellatrix had entered into an arranged marriage, a loveless one to a man she despised, a man who she did not see as her equal, and she felt bored and stifled and resentful. And then Voldemort came along and offered her everything- a chance to please her family, but still explore magic and set light to her talents. And she fell for him, and wanted to prove to him she was worthy because she still had this inbuilt need to please.
She was proud and arrogant and had a passionate obsession for giving her all, because then maybe Voldemort would show her the love she craved, but she couldn't see that Voldemort could see all this and used it to his advantage. And she sank darker and darker.
I also believe there may have been the loss of a child somewhere. It made no sense to me that she wouldn't want to do her duty and produce a pureblood heir. And then in Half Blood Prince she mentioned not having sons, which made me suspect she had miscarried or lost a daughter in infancy.
I don't believe she intended to send Frank and Alice mad. Because in doing so she failed...She didn't get the information she needed. She just lost control.
I don't believe the Bellatrix of the first war was the same person as the Bellatrix of the second war. Azkaban damaged her; Azkaban sent her mad. But even in the second war there were vestiges of the witch she had been; she was talented and astute, but she feared Voldemort as much as she loved him and the fear drove her to more and more out of control behaviour.
I genuinely think had Bellatrix met a Ted, she could have made different choices. I never felt she was predestined for evil in the way Voldemort was.