Why did Gothic cathedral walls dissolve into colored glass?

Because one abbot wanted his church full of light, and the engineering that let him have it kept improving for a century. Stained glass itself was old: as early as 675, an English monastery had brought in workmen from France to glaze its windows. What Abbot Suger changed, when he rebuilt the Basilica of Saint-Denis near Paris, was the structure around the glass. He designed a choir that would be suffused with light, and his masons combined features already found in Romanesque building, pointed arches, ribbed vaults, clustered columns and flying buttresses, which made room for large windows high in the walls. Dedicated in 1144, the building became the prototype for others in northern France and is often cited as the first Gothic building. Its rose window is the earliest known example of the form.

Others took the idea further. After a fire in 1194, Chartres Cathedral was rebuilt with flying buttresses supporting its upper walls, which were filled with stained glass telling the story of the Virgin Mary, a small corner of each window showing the craft of the guild that had donated it. In the High Gothic cathedrals that followed, the whole upper band of windows, the clerestory, was given over to glass, rose windows grew larger, and flying buttresses reached up to the highest windows. Height had its limits: the choir of Beauvais Cathedral, at 48 metres, outdid Chartres's 38, but part of its vaulting collapsed in 1284.

The other path was coverage. From the 1230s, the style called Rayonnant Gothic maximized stained glass until walls were effectively entirely glazed, as in the rebuilt nave of Saint-Denis and in the Sainte-Chapelle in Paris, the royal chapel of Louis IX built around 1241 to 1248, its expanses of glass reinforced with ironwork. The craft itself barely changed: pieces of glass coloured with metallic salts, held together by strips of lead. What changed was how little wall the architecture needed.