The reason people believe they have an element is because in the Western Mystery Tradition the zodiac signs all have elements assigned to them. Therefore people who are taurus will have an Earth sun sign, those who are pisces a water one.
The elements are merely a classification system for certain principles, and are not referring to the actual physical elements themselves, the physical elements are merely used as symbols for metaphysical principles.
What is more is your astrological chart will most likely have the planets in various constellations, and so you will have all sorts of 'elements' in your chart.
Fire signs- Aries, Leo, and Saggitarius.
Water signs- Cancer, Scorpio, and Pisces.
Air signs- Gemini, Libra, and Aquarius.
Earth signs- Taurus, Virgo, and Capricorn.
The problem is, that most modern traditions don't openly state where they borrowed their practices and beliefs from, I believe if people picked up Regardie's book on the Golden Dawn more or less everyone practicing path developed after the early 1900s will see some similarities.