The swastika is not a historical curiosity in the traditions that use it. It is drawn this morning, in wet vermilion or in rice flour, on thresholds and doorframes across India, on the covers of new account books at Diwali, on wedding invitations, on the tailgates of trucks, on the first page of a school exercise book and on temple walls. It marks the opening of an auspicious undertaking. The Sanskrit name is svastika, built from su, well, and asti, it is, with the sense of conducive to well-being, and the word is old enough to be discussed by Panini.
In Jainism it is the emblem of Suparshvanatha, the seventh Tirthankara, and its four arms are read as the four states into which a soul may be born: heavenly, human, animal and hellish. It is drawn in loose rice before an image as part of ordinary temple observance, and it stands at the centre of the Jain emblem itself.
In Buddhism it marks the footprints and the heart of the Buddha and appears in several enumerations of auspicious signs. In Japan it is the manji, and it is the standard cartographic symbol for a Buddhist temple; when the national mapping agency proposed dropping it from maps prepared for foreign visitors ahead of the 2020 Olympics, the objection was strong enough that it was retained for domestic use. In Tibet it occurs in both facings, and the left-facing yungdrung is the central emblem of Bon.
The figure is older and wider than any of these traditions. It appears on Neolithic pottery, on seals from the Indus Valley cities of the third millennium BCE, on Greek meander borders, in Roman mosaic, on Anglo-Saxon and Norse metalwork, on Baltic and Slavic textiles, in Ethiopian church decoration, and in the weaving, basketry and silverwork of several nations of the American Southwest. Most of these occurrences have nothing to do with each other. It is a shape that people who draw with straight lines arrive at independently, which is why it is everywhere.
None of that is the reason it is difficult to write about.