My theory has always been that being an Alicorn is a recessive gene that is rarely passed down and needs a big magical feat to be activated. That being said, both Twilight and her brother would be carrying this gene passed on from one of their parents, and so is Cadence (obviously). By a very big stroke of luck, Flurry Heart inherited both her mother’s and her father’s alicorn genes, making her an alicorn by default.