Questions: Girl's Behavior

She always thinks she knows everything better than I do even when I have more knowledge and formal education in an area after years of training. For instance she would insist that astrology can be proven through principals of physics and mathematics even though it is complete bullshit. She thinks she knows more about my college major (engineering science) than me even though she never even went to college nor does she read any books of any kind EVER. When I was in high school, every time I would get an A she would accuse me of cheating during an exam even though I NEVER did that. She always thinks she needs to explain simplest concepts to me when she is the last one in our family to understand them and even my father would get pissed at her low opinion of me. Funny thing is, when my little 8 year old brother is more skilled in a certain area, she has no problem admitting it and she never doubts his abilities. So why can't she accept my strenghts?