Chiron does not rule Virgo, Ceres does. There is no Virgo or 6th House energy in Chiron's Tropical or Draconic Discovery Chart, with the exception of the Draconic Gemini Ascendant falling in the Tropical 6th House, which probably relates more to the teaching aspect Chiron once you heal your "wound".
There is a severe misunderstanding of Earth Energy among Astrologers due to the lack of Earth-specific planets in the charts. Cynthia L.C. Wood's perspective on the 3 earth signs in her book "Earth Rise: The Case for Studying and Using Earth in Astrology" (something that I've incorporated into my own readings and Astrological philosophy for the past 3 years) highlights this. Capricorn is the sense of order that Virgo understands, selects, and refines in order for it to be physically manifested correctly (Taurus). In the same notion regarding physical form, Capricorn is the Astral Body, Virgo is the Etheric Body (vital body, Chakra systems, etc), and Taurus is the Physical Body as a whole/mass bound by gravity (Earth/Gaia Sign, always exactly opposite your natal sun, how you are grounded in physical reality and your physical vessel).
Dwarf planet Ceres, Mother of the Asteroid Belt, is the ruler of Virgo. I've seen some people claim that Chiron rules Virgo, but that doesn't make sense on a practical level. I personally think most astrologers place too much emphasis on Chiron and not nearly enough on Ceres and her Asteroid children (who all orbit our Sun in between Mars and Jupiter in a torus shape) or even other Centaurs (Chariklo and Pholus are also retrograding in Capricorn right now). Ceres, who is a true planet (is spherical due to her own gravity) is only called a dwarf planet due to her size. Ceres is significantly closer to Earth and larger than Chiron. Also, for a body in Ceres' location to have the same gravitational effect on Earth as Pluto (another dwarf planet), it would need to have a radius of at least 240 miles; Ceres' radius is 293.91 miles. Ceres is a geologically active proto-planet (baby/seed planet) that likely migrated from the Kuiper Belt, which is fitting if you know the mythology of Ceres (Demeter) and Pluto (Hades), who resides in the Kuiper Belt. Chiron is further out than Ceres and is significantly smaller, so it holds less weight in the System. Chiron and the other Centaurs in the solar system are hybrids of comets and asteroids orbiting from the Main Belt to the Kuiper Belt, and most link the orbits of other planets, serving as energies of transformation/transmutation of the planetary bodies involved. Their orbits are not stable, being disturbed by the gravity and orbits of the Outer Planets, so they will likely leave our Solar System all together in a few million years. This means that we will eventually evolve past their energies in this System and therefore our charts. Chiron itself links Saturn and Uranus, orbiting much closer to Saturn (fitting given the limits imposed by the wound Chiron places in our charts). Saturn and Uranus deal with social interactions and their planetary returns come much later in life, and Chiron itself only returns at about age 51, making it an energy that is reviewed and refreshed just prior to our second Saturn Return.
If anything Chiron andhis fellow Centaurs are like higher octaves of the Main Asteroid Belt, meaning we need to understand the inner belt a bit better before moving outward. Perhaps the objects in the Kuiper Belt are higher octaves of the Centaurs, as I suspect they may also relate/link specific sign energy. For example Pluto and its family and Haumea and its family both relate to different facets of Scorpio energy, perhaps one is of the Scorpion, the other of the Eagle. Similarly, while I believe Ceres rules Virgo, and all of the Main Asteroid Belt falls under Virgo, specific Asteroids link specific signs, mostly Leo through Scorpio (who tell the story of the kundalini): Juno is related to Water Energy in a blend of Libra/Scorpio (there's a difference between a Venus relationship and a Juno relationship), while Vesta (the parent body of the Vesta Family, a group of over 15,200 asteroids) is definitely Fire Energy, relating to our inner fire/hearth/charge/kundalini force, our focus and commitment, and the inner union and regeneration with the self; giving away our kundalini is the Scorpio/8th House realm. Vesta is so bright that she can be occasionally seen with the naked eye from Earth. Virgo energy sees and organizes the energies of how we begin to interact with others which is seen with Ceres and her belt of Asteroids, who are personal energies we utilize by directing our energy (Mars) before heading into the social sphere of Jupiter and beyond.
Ceres is currently retrograding in Pisces (at the exact degree Mercury retrograded back in Pisces Season) conjunct Nessus (another Centaur). Ceres is how we tend to our well-being, our sense of self-reliance, nurturing ourselves and others in a physical sense (Cancer/Moon is emotional; perhaps Ceres is exalted in Cancer), which includes the very simplified action descriptions of Virgo and the 6th House, routine, health, and service (caring for ourselves and others, like babies/pets or a garden, via a routine). The efforts we put in dictates the results of our harvest (what we're known for, the 10th House) and is usually seen in what we value (2nd House). Only a change in values that is met with appropriate action and done consistently (routine, 6th House) will produce the results that we want (10th House). There is far too little earth planet/energy representation in charts. Chiron represents a spiritual wound, and is important to understand, but we should definitely be focusing more on the physicality of our existence and day-to-day lives than on too much of the spiritual/internal. We live on an EARTH planet in a PHYSICAL reality after all and we sure have some environmental health issues on the mirco and macro levels right now.