Nurses were traditionally women because women cared for helpless babies and children and so seemed by extension to be the obvious carers for the helpless sick and aged.
There was also the other tradition of "wise women" who knew the uses of medicinal herbs (and the appropriate spells and incantations) and could set broken bones.
It was customary too. until comparatively modern times, to exclude men from assisting at the purely female experience of childbirth,, where the helpers needed a knowledge of anatomy and physiology, painkillers, and psychology. (the men would - shock horror - see the private parts of a woman who was not their wife)
Sick nursing was regarded as an "unskilled" occupation, which could be carried out by anyone with a minimum of instruction. When my mother worked as cook in a fairly upmarket nursing home in the twenties and thirties, most of their nurses were recruited in rural Ireland and were, as she put it, "straight off the farm". Their concept of hygeine related more to the byre than to the ward. That was not unusual. In those days of limited education and opportunities for women, there was always an inexhaustable supply of young girls looking for unskilled employment.
It takes a long time for the association of an occupation with one sex or the other to change. How many female steeplejacks (or even Prime Ministers) have there been?