- What sport are they training for?
Squatting is best done in the manner that gives the athlete the most carry over. This requires an understanding of the sport, and the athlete themselves. IF just squatting for the sake of squatting, then wherever the most power is generated...
- How is their body (and - more specifically - their legs) proportioned?
Longer legs and particularly femurs make squatting like a Chinese weightlifter impossible: the amount of space required for long legs at the bottom of the squat cannot be reconciled to the space availabe... it's simple physics. A wider stance effectively reduces the length of the femurs (due to the angle at which they're positioned), allowing more room to move. The other alternative is to flare one's knees and squat with more toe-out, but that can be quite contentious.
- What is their mobility like, and what is optimal?
If somebody has poor (or rather, average) ankle mobility, sqwuatting wide reduces the requirement for ankle flexion because there is not so much forward knee travel, meaning the positions being hit are less "compressed" than with a shoulder-width (ish) squat (again, dependent on leg/femur length).
- What is their hip anatomy like?
Some people just can't squat ATG, or get parallel in certain positions without compromising their lumbar stability, because their femur-acetabulum (hip socket) does not permit it. Some people's hip sockets point more or less straight down and are very deep, making pistol squats a doddle, but making a wide stance impossible; conversely, shallow, angled socked effectively allow for almost a complete ROM in any direction, meaning the lifter won't be limited by this...