Agriculture. Farmers need plows, hoes, scythes, pottery to store the harvest in, lots of stuff. The purpose of cities is to enable manufactoring by bringing suppliers for the various manufactoring processes close together
Especially hoes, practitioners of the world's oldest profession (actually, I think jewelers were first).
I think you're entirely correct: cities were the manifestation of agricultural life, when people could settle down and stop being nomads for a living. Technology like beer and bread require a settled life, with nutritional protein supplied by herds of domesticated creatures. (Prior to that, fermented mare's milk probably got everyone going on Saturday night). Since these discoveries were diffused around the populated world at approximately the same time, cities emerged everywhere roughly simultaneously.