 Solution

The intended ordinary-carbide comparison is energetic: the smaller, more strongly polarizing $\mathrm{M}{\mathrm{g}}^{2+}$ can stabilize a different balance of lattice energy and carbon-anion bonding from the larger $\mathrm{C}{\mathrm{a}}^{2+}$. Stabilization of the highly charged ${\mathrm{C}}_3^{4-}$ group competes with acetylide formation; electron counting alone does not require the same carbide stoichiometries for both metals. Ionic size and charge density provide a qualitative explanation, not a complete phase-stability calculation.

The literal claim that calcium has only one carbide is too broad. Primary calculations and high-pressure synthesis have established additional calcium carbides, including $\mathrm{C}{\mathrm{a}}_2{\mathrm{C}}_3$ and $\mathrm{C}{\mathrm{a}}_2\mathrm{C}$; known calcium-carbide chemistry also includes $\mathrm{Ca}{\mathrm{C}}_6$. Thus the conventional comparison must be limited to the familiar salt-like compounds and conditions intended here, rather than treated as a prohibition on other calcium–carbon compositions.^[ref]