**Core Concept**
The buffering capacity of a buffer solution refers to its ability to resist changes in pH when acids or bases are added. This is due to the equilibrium between the weak acid and its conjugate base. The buffering capacity is maximum when the pH is equal to the pKa of the weak acid, as this is the point where the concentration of the weak acid and its conjugate base are equal.

**Why the Correct Answer is Right**
When the pH is equal to the pKa, the equilibrium between the weak acid (HA) and its conjugate base (A-) is at its midpoint. The equation for this equilibrium is HA ⇌ H+ + A-. At this point, the concentration of H+ ions is equal to the concentration of A- ions, and the buffering capacity is maximum. This is because the buffer can easily accept or donate H+ ions to resist changes in pH.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the buffering capacity is not maximum at the lowest possible pH. In fact, the buffering capacity decreases as the pH deviates further from the pKa.
**Option B:** This option is incorrect because the buffering capacity is not maximum at the highest possible pH. The buffering capacity is maximum at the pKa, not at the highest pH.
**Option C:** This option is incorrect because it is not a valid answer choice.

**Clinical Pearl / High-Yield Fact**
Remember that the buffering capacity of a buffer solution is maximum when the pH is equal to the pKa of the weak acid. This is a key concept in understanding the behavior of buffer solutions in physiological and laboratory settings.

**Correct Answer:** C.