Jain tradition does not make a universal rule that only women should cover their head. Practices vary by tradition (Digambar vs. Shwetambar) and by region and customs, so you’ll see different expectations in different communities.

• In many Shwetambar communities, women more commonly cover their heads as a sign of modesty and respect during rituals, temple visits, or when in the presence of Tirthankaras. Men may cover their heads in some contexts too, but it is less universal for men.
• In Digambar communities, the monastic code for monks and nuns is separate from lay practice. Monks traditionally do not cover their heads in the same way laypeople might, and nuns’ dress and practices follow their own norms. Among laypeople, head covering is not a strict doctrinal requirement but may appear in certain regions or during specific ceremonies.
• The underlying reason is modesty, cleanliness, and reverence in sacred spaces, not a rigid gender rule laid out in Jain scriptures. The “why” is often tied to cultural norms about respect and humility rather than a fixed religious command.

If you’re looking for a precise stance in a particular Jain community or wish to see scriptural references cited by Digambar and Shwetambar scholars, tell me which tradition or region you have in mind and I can give a more detailed, tradition-specific explanation.