The thing "Mending Wall," "Elinor Rigby," and "Another Brick in the Wall" have in common is the themes of separation, loneliness, isolation, and dehumanization; this last is implied in the first and explicitly addressed in the last. A brief examination of each sheds light on the similarities. Though the last line of Frost's "Mending Wall" seems to advocate a good wall between people, Frost's speaker has earlier established his opposition and has tried to coax his neighbor into examining his adage: "Good fences make good friends." Frost’s speaker asks whether “fences making good neighbors” isn't in fact restricted to land with wandering grazing cows: "Isn't it / Where there are cows?"
He speculates that his apple orchard and the neighbor's pine forest won't bother each other and so don't need to be walled apart: "He is all pine and I am apple orchard." He concludes by saying of his neighbor:
He moves in darkness as it seems to me-- ...
He will not go behind his father's saying,
This is the speaker's pronouncement that his neighbor will not, perhaps can not, examine his belief ("go behind his father's saying") and will continue to impose isolation, separation, and its resultant loneliness through perpetually mending the wall that nature and man instinctively tear down:
Something there is that doesn't love a wall,
That sends the frozen-ground-swell under [ground swell: frost heave that moves the earth upward] ...
The work of hunters is another thing
In "Eleanor Rigby," the Beatles describe the isolation of both Eleanor and Father Mackenzie. Eleanor is dreaming of the day ("Lives in a dream") that she can have a full and vibrant life that is connected to other people but can only come close enough to collect traces of others’ lives: "picks up the rice in the church where a / wedding has been." She waits "at the window," looking her best, for a visitor who never appears ("Who is it for?"). Similarly, Father McKenzie works diligently on his Sunday sermon although no one attends his church anymore:
writing the words of a sermon that no one will hear--
No one comes near.
These two isolated, lonely, separated souls meet, sadly, at Eleanor's funeral where Father McKenzie performs her burial rites alone at the graveside.
Father McKenzie wiping the dirt from his hands as he walks from the grave
Whereas these two poems range from speculative examination to lamenting melancholy, "Another Brick in the Wall" is a brutal poem as well as being about brutality causing isolation, separation, and loneliness. In addition, the aspect of brutality results in the inclusion of dehumanization. It is in a restricted sense a child's poem--not suited for children to read (or hear sung) but about children. Pink Floyd tells of children subjected to hurt and derision at school administered by teachers themselves brutalized at home:
teachers who would hurt the children anyway they could ...
when they got home at night
Would thrash them ...!
It is a brutal poem (ironically administering an emotional thrashing of it's own through vocabulary and imagery even as it protests against brutality) pleading for a proper perception of the brutality that causes the separateness, loneliness, and isolation. The final statement is that such brutality occurs because individuals are wrongly perceived as "just bricks in the wall," one part of the double metaphor of "wall." "[B]ricks in the wall" represents the dehumanization the poem protests.