Here are 6 good reasons to avoid tailwinds whenever you can...

1) Increased Groundspeed

Higher groundspeed on final approach all the way through touchdown makes landing on your intended point more difficult.

2) Increased Rate Of Descent

Because of this increased groundspeed, if you're flying a final approach with a tailwind, you'll be forced to fly a increased rate of descent. This can make it difficult to perform a stabilized approach.

3) Increased Takeoff Distance

According to a Cessna 172S POH, you should expect a 50% longer takeoff roll with a 10 knot tailwind.

4) Increased Landing Distance

The same goes for landing. For each 2 knots of tailwind in a C172S, add an additional 10% to your landing distance. In the video below, a Boeing 737 floats almost all the way down the runway during a landing in Tegucigalpa, Honduras. The extra groundspeed this aircraft had during landing is the same factor that causes many tailwind related accidents...

5) Reduced Directional Control

As you enter your flare on landing with a tailwind, you'll be traveling much faster over the ground than you're probably used to in your airplane, due to a high groundspeed. Maintaining directional control can be difficult, especially with a quartering tailwind.

6) Poor Obstacle Clearance

While your rate of climb won't necessarily change with a tailwind, your angle of climb can shift dramatically. If you have a strong tailwind, and a high groundspeed, your angle of climb is decreasing. That can make it harder to clear obstacles ahead of you.