My [17M] sister [18F] admitted to always hating my existence, because I was adopted. According to her that doesn't make me her real brother. I feel rejected.

I was adopted by her mum at a very young age. We grew up together, and she's always been a part of my life. Our family consists of just the three of us. My mum has always treated me kindly, but my sister was a different story. From as early as my memory allows me to recall my sister and I argued a lot, more often than most siblings would. I was bullied by her many times when we were little. I still loved her though, because she was my big sister, and my only other family member.
Over the years the bullying stopped, and we grew distant from each other, but my desire to connect with her never stopped. My sister has always been my role model, she's smart, attractive, gets good grades and has a very likable personality. I wanted to be able to talk to her about anything, but she expressed discontent in that idea and I backed away.
My sister is going off to university when she graduates school this year, and will be away for a long time. It's my last chance to connect with her and form some sort of meaningful relationship. I tried starting a conversation last night, but she got mad at me, and we had an argument. This argument felt different, because she truly meant what she said. She admitted to always hating my existence, because I was adopted, and that doesn't make me her real brother. In her eyes, I've always been a stranger. I started crying, and my sister didn't care, she told me to leave.
It’s a Saturday afternoon, and instead of playing video games I'm in my bedroom sobbing over the fact that my big sister, someone I've always looked up to and forever wanted a connection with, hates my guts. I don't understand. Why does my sister hate me? Why does she despise my very existence over something I had no control over?
I hear all my friends talk about how close they are with their siblings, and it truly makes me depressed comparing their situation to mine.
I've only ever wanted to have a friendly sibling relationship with my sister. I want to be close with her, but at this point I just want her to accept me as her brother. I fear it'll never happen. For the rest of my life I'll miss out on that special brother-sister connection with the only sister I'll ever have.

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tl;dr: My sister admitted to always hating my existence because I was adopted. Despite the fact that we grew up together as children she has never thought of me as her brother. I feel rejected and bad about myself.


Source.

Balls....grow a pair