Why do we always implement the complementary of the boolean expression when we design a CMOS circuit?
Complementary does not mean there is an inverter circuit.
Complementary means, there are both NMOS and PMOS transistors, as logic that existed before CMOS had only NMOS transistors.
In a CMOS circuit, NMOS transistors are able to pull strongly low, and PMOS transistors are able to pull strongly high.