Follow the logic through....
Assuming, first of all, that a spoiler does in fact generate downforce - many don't.
Now, take that spoiler and add it to the rear of a front-wheel drive car.
Under acceleration, weight shifts to the rear of the car, off the drive wheels. At a given speed the spoiler starts to generate noticeable downforce on the rear of the car, transferring yet more weight off the drive wheels.
Now you have a car whose driven wheels have little weight above them. This means acceleration occurs at a decelerating rate, because of a decreasing contact patch with the road. You've also got less weight on the wheels for turning - hence a big, functional rear spoiler on a front-wheel drive car leads to LESS grip and stability.
For the most part, added aftermarket spoilers aren't functional. This has the sole effect of placing an object in the airstream of your car, decreasing the aerodynamics and increasing the frontal area, leading to an increase in air resistance and a corresponding DROP in performance.