A horse can only work so many hours. Scheduling lessons without tracking which animal has already done four is how horses get injured and how a school loses its best pony for a month.
Matching is the daily decision. Ability, confidence and weight determine which horses are suitable for which rider, and getting it wrong is either dangerous or discouraging enough to end somebody's riding.
Livery is a monthly contract with a long tail of extras. Feed, bedding, farrier visits, worming and rugs added to a standing fee: billed from memory, half of them are never charged.
Bad weather cancels a day, not a lesson. An unusable arena or frozen ground affects everybody booked, and rescheduling twenty riders is a single decision rather than twenty conversations.