Être à cheval sur
The French expression être à cheval sur quelque chose translates literally to "being on horseback about something." As you may guess, however, its idiomatic meaning has nothing to do with saddling up for a ride. It is used to describe someone who is a stickler for something, particularly rules, details, or principles. Imagine someone so focused on following rules that they are practically galloping on their high horse, clipboard in hand, making sure everyone is dotting their i's and crossing their t's. They might as well be wearing a helmet and a saddle, ready to charge at any sign of disorder!
Origin
The expression être à cheval sur indeed has origins linked to the world of horsemanship and specifically to the strict rules and standards of dressage, which is the practice of training horses to perform precise movements.
Dressage is highly regimented, requiring both horse and rider to adhere to precise movements and positions. A rider must be à cheval sur (a perfectionist about) their posture and the execution of commands to ensure the horse performs correctly because every bend and trot is meticulously judged against a ruler-straight standard. Over time, this horseback obsession with perfection seeped into everyday life to describe someone who is similarly strict or meticulous in other contexts, such as rules, principles, or standards unrelated to horses.
Note: à cheval sur shouldn't be confused with à cheval entre - that's a whole different horse ride. Être à cheval entre - to be on horseback between - means to be at the boundary or edge of two distinct areas, whether literally, or figuratively. The spatial meaning is the most common and might refer, for example, to a village split between two counties, or a house being half in the city and half in the boonies. Figuratively, "Être à cheval entre deux choses" directly refers to being torn between 2 viewpoints or 2 options, indicating a state of indecision.
Whether you're riding high on strict rules or straddling two counties, "être à cheval" is a phrase that's got all the bases covered.
Examples
Il est à cheval sur la ponctualité.
He is very strict about punctuality.
Elle est à cheval sur la propreté.
She is very particular about cleanliness.