Why do I need a base case for n=3 when solving a d&c recurrence?
They do not want $T(1)$ to occur as a base case as it causes troubles. $T(3)$ depends on $T(1)$, so if they didn't take $T(3)$ as a base case in addition to taking $T(2)$ as one, they'd run into trouble when applying the inductive step to $T(3)$ as the hypothesis does not hold for $T(\lfloor{\frac{3}{2}}\rfloor)=T(1)$.