Despite the importance of the on-surface Ullmann coupling for synthesis of atomically precise carbon nanostructures, it is still unclear whether this reaction is catalyzed by surface atoms or adatoms. Here, the feasibility of the adatom creation and adatom-catalyzed Ullmann coupling of chloro-, bromo-, and iodobenzene on Cu(111), Ag(111), and Au(111) surfaces is examined using density functional theory modeling. The extraction of a metal atom is found to be greatly facilitated by the formation of strong phenyl-metal bonds, making the extraction energy barrier comparable to, and in the case of Ag(111) even lower than, that for the competing surface-catalyzed phenyl-phenyl bond formation. However, if the phenyl-adatom bonds are too strong, as on Cu(111) and Ag(111), they create an insurmountable barrier for the subsequent adatom-catalyzed C-C coupling. In contrast, Au adatoms do not bind phenyl groups strongly and can catalyze the C-C bond formation almost as efficiently as surface atoms.