He was advocating Indians spinning and weaving themselves rather than exporting to England who would import it back making ridiculous profits.

I can't find many mentions of spinning in Indian culture, though those that do involve women, such as mentions of women spinning while men are away. Spinning with a spindle is listed among important arts, though I don't know how significant that is and why specifically a spindle when India has had spinning wheels since forever.

In practice all genders weave, which doesn't mean there isn't gendered symbolism.