If you and your neighbor are equally responsible for the fence, it would be beneficial to draft a formal agreement outlining how decisions will be made and who will bear financial responsibility for the fence. Believe me, this will save you a tremendous amount of stress and potential conflict down the road.

Examples of Situations Where the Finished Side Does Not Face the Neighbor
This is the point at which the “always face the neighbor” rule begins to break down. There are numerous legitimate situations in which someone may not have the finished side of the fence oriented toward their neighbor. Examples include:
Good neighbor fences (double-sided) are designed to appear the same on both sides of the fence. Therefore, neither party is disadvantaged.
Private concerns (such as obstructing views or supporting tall panels) may necessitate placing the fence posts inside to provide additional structural reinforcement.
Sloping terrain may require changing the orientation of the fence to accommodate the topography of the land.
Cost factors may cause an individual to select a less expensive type of fence that does not have a visually appealing side.Patio, Lawn & Garden
Trees, sheds, or other obstructions may limit where and how the fence is installed.
There are even instances in which individuals choose to install fences backward for security purposes. When rails are on the inside of the fence, it becomes more difficult to climb.
Best Practices I Would Suggest Prior to Constructing a Fence
After experiencing this process myself, this is what I wished I had known prior to calling the contractor:
Check local ordinances before installing a fence.
Speak to your neighbor if the fence will be located along a shared boundary line. It is simply polite.
Clearly mark your property boundaries, regardless of whether you need to hire a surveyor.
Consider aesthetic appeal from both sides. You will live with this fence for years.
Document any agreements regarding the installation of a shared fence in writing.

Does the Finished Side Have to Be Facing the Neighbor?
Based on all of the research and experience I went through, I believe that the finished side of a fence is usually oriented toward the neighbor. However, it is not a hard and fast rule. Sometimes it is a law, sometimes it is a matter of etiquette, and sometimes it does not apply at all.
If you are unsure, and I know I was, I suggest leaning toward courtesy when possible. However, I would recommend making decisions based on your local ordinances, your property line, and a little friendly communication. A good fence may create a good neighbor; however, a good conversation creates an even better neighbor.