Rebecca's bioploar disorder?

Bi-polar disorder is from a chemical imbalance in the brain - just because one has a loving "normal" family doesn't mean they can't be seriously mentally ill. Seeing her parents it's unlikely that she got it from them - then again, either one could have been on meds to balance their own disorder, but since we didn't see much of them, there could be a time when one of them was depressed. However the way they show it in the film is that Rebecca was pretty much born with it and has suffered her whole life with this illness.
Hope that helps :)

One can grow in a wealthy mansion with 2 loving parents and being a bipolar person ...

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What is an ocean, but a multitude of drops ?

Bipolar disorder isn't created by bad parenting. There's still some unanswered questions about where it comes from but it usually can be traced down to genetics or physical imbalances in the brain. Unhealthy parenting environments can exacerbate the symptoms that are already there, but people with good parents can still get the disease.

Not all BPD cases are the same. BPD sufferers can experience out of control mood swings or different manias. Very few BPD sufferers are homicidal.

In Rebecca's unique case, even though she kills, she should not be lumped in with psychopaths. Rebecca can feel remorse, but the BPD distorts her view of what's going on around her. She saw Sarah going out with other friends as Sarah abandoning her, and she believed that she was helping Sarah by getting back at the people who hurt her. People who suffer from BPD or other related diseases might feel over-defensive: because their erratic behavior drives other people away, an undiagnosed BPD can perceive that other people are snubbing them or mistreating them, and they don't understand why.

BPD sufferers often don't like to take their medication because the medication sometimes has unpleasant side effects. Thankfully, medications have improved in the last twenty or thirty years.