White is the hardest of the basic colours to obtain as a durable paint, which is not obvious until one tries.
Chalk and lime are cheap, safe and available everywhere, and they are the whites of the plastered wall and the limewashed church. In oil, however, chalk turns nearly transparent, so the medium that dominated European easel painting for five centuries could not use the cheap white at all.
The white that worked was lead white, basic lead carbonate, made by exposing coiled lead strips to vinegar vapour and animal dung in sealed pots, a process described by Theophrastus and still recognisably the same in the eighteenth century. It is opaque, it dries well, it handles beautifully, and it is a cumulative poison. It was also the standard cosmetic base for skin whitening in Europe and in Japan, applied directly to the face for centuries.
Titanium white, titanium dioxide, arrived commercially in the early twentieth century and is more opaque than lead white and not toxic. It displaced lead white for almost all purposes within a few decades, and conservators can now sometimes date a painting by which white is present in it.
For cloth, white was a matter of bleaching rather than dyeing, and bleaching before industrial chemistry meant months of washing and laying out in the sun. Undyed cloth is not white; it is grey or yellowish. That is worth holding onto when reading any tradition in which white garments mark purity, since the whiteness was itself the expensive part.