DIY electrical guy here. I have one 2/12 coming into the top of an existing wall switch (sgl. pole) that powers an existing light fixture. So I assume (right or wrong) that the current is coming into the switch on the black side and (when switched on) follows the common wire back to the black side of the 2/12 running over to the light fixture. Since the voltage after the switch is carried on the white side, I spliced my exhaust fan into the white side of the romex between the switch and the black side of the 2/12 running out to the light fixture. In my thinking, I figured the existing switch would power my new exhaust fan AND the light fixture. But after flipping the 15A circuit breaker back on, the switch still worked the light fixture, but the fan wasn't working right. The fan blade turns, but not with enough force to move any air. Where did I screw up? The fan works, by the way. I checked it by plugging it into an outlet and it moves 70CFM no problem.
They should be wired in parallel instead of being in series.
The light bulb is limiting the amount of current that can run the fan, like a resistor.
Kudos on including that diagram. It makes the situation very clear. Upvote.