# "Why do they say the stronger the acid, the stronger the conjugate base?"

Presumably, they simply made a mistake. Are you sure they didn't say, $\text{the weaker the acid, the stronger the conjugate base}$?
As you know, $p {K}_{a}$ and $p {K}_{b}$ are logarithmic functions, and are defined by the relationships, $p {K}_{a} = - {\log}_{10} {K}_{a}$, $p {K}_{b} = - {\log}_{10} {K}_{b}$.
Given this definition, it follows the smaller, that is the more negative, the $p {K}_{a}$ value, the STRONGER the acid is. It is a bit counter-intuitive, and we have all made mistakes in interpretation.