St. Thomas Aquinas
“Barley bread serves to denote the hardness of the Old Law; both on account of the hardness of the bread, and because, as Augustine says: ‘The flour within the barley, wrapped up as it is within a most tenacious fibre, denotes either the Law itself, which was given in such manner as to be vested in bodily sacraments; or else it denotes the people themselves, who were not yet despoiled of carnal desires, which clung to their hearts like fibre.’ But this sacrament belongs to Christ’s ‘sweet yoke,’ and to the truth already manifested, and to a spiritual people. Consequently barley bread would not be a suitable matter for this sacrament.”
Source: St. Thomas Aquinas, Summa Theologica