I was raped by my older brother when I was 13. He'd abused me sporadically for years, but as he was easily always a foot taller and a hundred pounds heavier, fighting back was difficult and usually resulted in me being punished if he had any bruises or scratches on him. By the time the actual rape occurred, I'd long since realized it was futile to tell anyone.
When I was a senior in high school, I confided in my counselor who'd sworn to me everything between us was confidential. Well, unfortunately it wasn't, since I was a minor and my brother lived at home with my mom and I still. I went to school the next day, was called to the counselors and was informed they'd called the police, they were on their way, and so was my mom. My brother was in custody, and astonishingly... He'd confessed. My mom came in, saw me bawling and panicked, asking me what was wrong. The police made me explain, and her entire demeanor instantly changed. She insisted I was lying, despite the confession, that I must have "done it to myself" (wtf does that even mean?), and worst, just crying inconsolably that her "baby" was being treated that way. We all went through years of counseling, together and separately. I chose not to pursue a trial after I was told to testify and badgered by cops that if I committed perjury at all and was "making it up for attention", I'd go to jail myself. My family was destroyed as it was, everyone in school had found out, I was suicidal and I couldn't handle all that. I never intended to pursue any legal recourse against him anyway, I had always planned on moving out at 18 and being away from it all. My brother went to live with my father, where he still lives. I stayed with my mother until everything resolved with the police, then she kicked me out with two trash bags of my stuff to my name and that was it. I didn't speak to any of them for a year, and I'm slowly rebuilding my relationship with my parents since they're elderly and need help. It's tough. I regret confiding in the counselor, though she had the best of intentions, it shattered my trust in authority for years and made my situation infinitely worse than it was.
Tl;Dr: My parents would rather believe that their daughter is a pathological liar than that their son is an incestual rapist.