Why can nerve impulses travel only in one direction?

Because of the chemical nature of impulse and the axon-dendrite structure.

Because of the chemical nature of impulse and the axon-dendrite structure.http://www.biologymad.com/nervoussystem/nerveimpulses.htm (Best technical explanation and excellent graphics and animations)

The best generic answer from a 2008 post follows (with my own edits for clarity):

A Nerve electrical impulse only travels in one direction. There are several reasons nerve impulses only travel in one direction. The most important is synaptic transport.

In order for a "nerve impulse" to pass from cell to cell, it must cross synaptic junctions. The nerve cells are lined up head to tail all the way down a nerve track, and are not connected, but have tiny gaps between them and the next cell. These tiny gaps are called synapses.

When you get a nerve firing, you have probably heard that it is an electrical impulse that carries the signal. This is true, but it is not electrical in the same way your wall outlet works. This is electrochemical energy. Neurotransmitters are molecules that fit like a lock and key into a specific receptor. The receptor is located on the next cell in the line. When the neurotransmitter hits the receptor on the next cell in line, it signals that cell to begin a firing as well.

This will continue all the way down the length of the nerve track. In a nutshell, a nerve firing results in a chain reaction down the nerve cell's axon, or stemlike section. Sodium (Na+) ions flow in, potassium (K+) ions flow out, and we get an electrochemical gradient flowing down the length of the cell. You can think of it as a line of gunpowder that someone lit, with the flame traveling down the length of it. Common electrical power is more like a hose full of water, and when you put pressure on one end, the water shoots out the other.

Therefore, nerve impulses cannot travel in the opposite direction, because nerve cells only have neurotransmitter storage vesicles going one way, and receptors in one place.

https://answers.yahoo.com/question/index?qid=20080916232931AA4zPLL