A wing upside down is only the start of the story
What an inverted aerofoil does, and what it leaves unexplained.
An aircraft wing turned upside down and mounted on a car produces downforce instead of lift because it is still the same curved, angled shape asking air to speed up over one face and slow down over the other, only now the low-pressure face points down toward the road. That flip is only the beginning of what decides how well the inverted shape works.
Which face gets the fast air
A wing generates a force perpendicular to the airflow by shaping the air's path so that it moves faster over one face than the other. By Bernoulli's principle, faster-moving air exerts less pressure on the surface it passes, so the wing is pulled toward its faster face and pushed by the relatively higher pressure on the other. An aircraft wing puts the faster air over the top and is pulled upward. Mount the identical profile upside down on a car, angled the same way to the oncoming air, and the faster air runs underneath, pulling the wing toward the road. The mechanism is unchanged between the two cases; only the choice of low-pressure face differs. An aircraft designer and a race car aerodynamicist can therefore look at one cross-section and call it a lift shape and a downforce shape respectively, and both are describing the same physics.
Feeling angle through a kite string
Flying a kite makes the sensitivity of this force to angle easy to feel through the string. Tilt the kite's face to catch the wind at the right angle and it pulls strongly and steadily. Change that angle and the pull weakens, strengthens or even reverses, although the wind itself has not changed at all. A car wing responds to its own angle just as sensitively, so inverting the shape settles only which way the force points. How strong the force will be at the angle and speed the wing actually runs at is a separate matter. Let the string out so the kite flies higher, into steadier wind, and the pull becomes stronger and more consistent than it was low down near trees and buildings, which maps directly onto the difference between a wing in clean air and one sitting in the disturbed air coming off everything mounted ahead of it.
Why a borrowed aircraft profile underperforms on a car
An inverted aircraft profile is tuned for conditions a car wing rarely sees. An aircraft wing is optimised for one steady cruising condition held for hours, in clean air, far from the ground relative to its own size. A car wing usually runs much closer to the ground, sits in air already disturbed and accelerated by the rest of the car, has to work across a range of angles as it is adjusted for different tracks, and must keep working through braking, cornering and acceleration, each of which changes the air arriving at it within seconds. All of these push car wing design toward shapes and angles an aircraft designer would rarely choose, even though the force-generating mechanism is identical.
The kite shows one more limit that matters here. Tip its face too steeply into the wind and the pull suddenly slackens and the kite wobbles, because the air can no longer follow its back surface smoothly and breaks away into a churning wake. A wing does the same thing, and the aircraft name for it is a stall. An aircraft spends almost all its life at gentle angles well clear of that edge, while a car wing set up for a slow, twisty track is often wound up to the steepest angle its designers dare, which puts it much closer to stalling. A car profile therefore has to be shaped to keep the air attached to its underside at angles an aircraft wing would only meet in trouble.
This is why a Formula Student wing profile taken straight from an aircraft handbook, however correctly inverted, rarely performs as well as one developed for close-to-the-ground running in disturbed air across a range of angles. The inversion explains the direction of the force, while its size, and how well it holds up in real conditions, depend on everything the handbook profile was never designed for. Flipping a well-known profile is a perfectly reasonable first wing, provided it is treated as a first guess and the real design work continues from there.