Men's shirts fasten right over left and women's fasten the other way. The convention is universal across the industry and has no functional justification in modern clothing.
The historical explanations are plausible but unproven
The most repeated account is that wealthy women were dressed by servants, and reversing the closure suited a helper facing the wearer rather than the wearer's own hands.
Another points to riding side-saddle and to the direction of prevailing wind, and a third to the way infants were traditionally carried and fed.
Each is coherent and none is documented well enough to settle the question, which is common for conventions that predate written manufacturing standards.
The convention was locked in by production
Once tailors and later factories standardised patterns, the closure direction became part of the pattern block rather than a choice made per garment.
Every downstream process assumed it. Buttonhole machine placement, cutting layouts, interfacing shapes and the direction of overlap in a placket all follow from it.
By the time anyone might have questioned the logic, the cost of changing it had become a manufacturing cost rather than a design decision.
Signalling kept it useful
The direction became a fast marker of whether a garment belongs to menswear or womenswear, and buyers and retailers both use that signal.
A garment fastening the unexpected way reads as borrowed or as deliberately unisex, which is an effect designers sometimes use on purpose.
Because it carries meaning, removing it would remove information, and there is no commercial pressure to give that up.
Zips and modern closures broke the pattern
Zips have no side convention in the same way, and their placement is driven by where a garment needs to open rather than by tradition.
Side and back zips in womenswear were once standard and have retreated as knits and stretch fabrics reduced the need for a full-length opening.
The button convention survived precisely because buttons stayed, while other closures arrived after the convention stopped being enforced by habit.
Where it still creates friction
Unisex and gender-neutral ranges have to pick one direction, and whichever they choose reads as gendered to part of the audience.
Some brands standardise on one side across the whole range, which simplifies production and quietly removes a distinction the market never asked for.
The convention persists mostly because it is invisible until pointed out, and inertia is sufficient explanation once the original reason has been forgotten.