Does it often happen that sisters hate each other from the start?

No matter how hard I try to build a relationship with my sister, it fails. This seems like a crazy question for a woman in her 40s but it still bothers me. I'm older by 3 years and she is much quieter and more introverted than I am. I chose a very difficult career, studied and became very independent with much travel and friends. She married in her late 30s (after several serious relationships), had a child and is now going through a dreadful divorce. At one family event 15 years ago she came up to me and said 'look at you! you look fantastic, you've got a prestigious job and I have nothing'. This hurt me as she looks great and chose a smaller job (she has a complex I think). I've tried inviting her for coffees when I'm in town but it always falls through and I feel she's making excuses and still actually hates me. Is this normal? What should I do?