Step 1: Chemical Reactivity
Aluminum has a very high affinity for oxygen.
Step 2: Thermodynamic Analysis
The enthalpy of formation of $Al_{2}O_{3}$ is extremely high (very negative), meaning the Al-O bond is exceptionally strong.
Step 3: Comparison with Carbon
Carbon is not a strong enough reducing agent to overcome this high enthalpy and displace oxygen from alumina.
Hence, the Answer is: (D)