Answer
The error is that pressure and volume are inversely proportional only if the amount of gas and temperature remain constant.
We think pressure and volume are inversely proportional due to the ideal gas law which states $PV=k \Rightarrow P=\frac{1}{V}k$.
Work Step by Step
In this scenario, we are increasing the amount of gas in the tires. Therefore, volume and pressure are both allowed to increase as the number of moles of gas, n, is increasing.
We think pressure and volume are inversely proportional due to the ideal gas law and the relationship that $P=\frac{1}{V}nRT$. However, this is only true when $n$ or $T$ is constant. However, in this scenario, we are increasing the number of moles of gas, n. Therefore, $P$, and $V$ are both able to change.
