Why is volume inversely proportional to pressure?
Given you know and understand Charles' and Gay-Lussac's laws, it's not about chemistry, rather, simple ratios:

$$
\begin{cases}
T \propto V\\
T \propto p
\end{cases}
\implies
p \propto \frac 1 V
$$

which, as Zenix commented, is a math form of Boyle's law.