An intersex person is one who is born with or develops mixed sexual physiology (an abnormally small penis, large clitoris, closed vaginal opening, separated scrotum, etc.). If discovered at birth, the child's gender is decided either by the surgeon or by the parents. Some intersex individuals do not discover they are intersex until they reach puberty.
In either case, many intersex people are raised as male or female even though they have the feelings or the internal anatomy of the opposite sex. It's very plausible for many intersex individuals to feel as if they were raised as the wrong sex.
Learn more about intersex.