The way in which a wall can be torn down between two individuals is for each to have the ability to see and accept the differences with one another. Because neither speaker nor neighbor achieves this in the poem, the wall remains between them. Ironically, however, this very wall between the neighbors is the same wall that ties them together with a similar interest, that being the annual mending of the wall. So you see, although the wall remains between them, it also joins them together by sharing in the mending of the wall, which in turn prompts them to repeat the same questions in the poem: speaker, "Something there is that doesn't love a wall," and neighbor, "Good fences make good neighbors." Without even realizing it, the repetition of questions and the mending of the wall, unite the speaker with the neighbor. In summary, developing an appreciation and/or understanding of someone helps to tear done those "walls" that create barriers between people.
The stone wall in the poem is not the only wall that stands between the speaker and his neighbor. They are quite different in their philosophies, and they do not understand each other's beliefs and feelings.
One way they could bring down this second wall between them would be to listen to each other, to really consider what each has to say. Instead, the speaker and his neighbor each hold on to their own points of view without really listening to the other. The speaker maintains, "Something there is that doesn't love a wall," while his neighbor repeats, "Good fences make good neighbors."
Active listening requires a dialog. Each man could simply say, "Why?" Why do good fences make good neighbors? Why do you think this is true? Why is there something that doesn't love a wall? What would that something be? If they talked to each other rather than at each other, they might begin to understand each other's point of view.
It is easier to respect that which we understand. If the speaker and his neighbor understood and respected each other, there would be no real wall between them, even if they disagreed.