Intuitively, it is pretty clear that you spend more time going against the wind than with the wind for an out-and-back course, so you can't possibly make up the lost time.
In addition, a headwind hurts your road speed more than an equivalent tailwind helps it.
The power required to overcome aerodynamic drag increases with the square of the speed increase. So, given the same power output, even though your "airspeed" decreases with the tailwind just as much as your "airspeed" increases with the headwind, your road speed is decreased more by the headwind than it is improved by the tailwind.