Monoborracho is correct. The problem with wind (or hills) is that in order for a tailwind to cancel out a headwind you have to average over time, but with any round trip you are averaging over distance.
Consider a twenty mile out and back round trip that you can do in exactly one hour with no wind (a 20 mph average speed obviously). One particularly windy day you set out into a terrible headwind. You can only maintain 10 miles per hour. The trip out will take one hour. There is no way you can average 20 mph for the whole trip now. You could go one thousand miles an hour on the way back and it would still take over an hour for the whole trip.
However, let's say after you make the turn around you can hold 30 miles an hour on the way back. If you were to maintain this speed for one hour (the same amount of time you spent on the way out) you would have covered a total of 40 miles (10 out and 30 back) in two hours for an average speed of 20 miles per hour, the same as you do with no wind. This is averaging over time.
This is the way it would work with a plane, but a bike has an additional reason why a wind will slow your average speed. The rolling resistance of a bike goes up as the speed increases regardless of what way the wind is blowing. The bearings in the wheels, wind resistance of the spokes, and friction of the tires on the road will mean that you won't be able to maintain 30 mph on the way back, maybe only about 28-29 mph. This means that even if you did spend one hour riding into the wind and one hour riding with the wind, you would probably come up slightly short of your average speed with no wind.