Several grammatical structures repeat throughout the poem—a device known as parallelism. The speaker also often parallel grammatical clauses in order to draw contrasts between opposite ideas, which is an example of antithesis.
In general, the speaker uses antithesis to differentiate anyone and noone from the rest of the townspeople. For instance, line 4 reads:
he sang his didn't he danced his did.
The construction of the two clauses here is exactly the same. Only the specific verbs change, and they are opposites: didn't vs. did. Three lines later, this is followed up with another example of antithesis, here with "sowed" and "reaped" being essentially opposites:
they sowed their isn't they reaped their same
While anyone expresses himself through song and dance, the townspeople are hard at work planting and harvesting (likely metaphorical) crops. As such, anyone appears to live a more emotionally honest and joyous life relative to his peers, who are preoccupied with labor.
Further, anyone laments all that he is unable to achieve ("his didn't") and celebrates all that he is able to do ("his did"). The townspeople, on the other hand, actively make sacrifices ("their isn't") in the name of a more distant reward—"their same," which might be a reference to the idea that they all have the same desires in life, or that their lives are unrelentingly monotonous.
Later, in line 10, the speaker explains that as children grow older, they begin to disregard the relationship between anyone and noone:
and down they forgot as up they grew
Here, antithesis accentuates the contrast between "down" and "up." In doing so, it emphasizes the children's loss of care and suggests that aging—growing "up"—is to blame for their apathy.
When describing the strengthening bond between anyone and noone, the speaker remarks:
she laughed his joy she cried his grief
In this case, antithesis exaggerates the highs and lows that the couple endures to demonstrate the range of experiences that they have had together. At the same time, the juxtaposition of anyone' s "joy" and "grief" plays up noone's capacity to empathize with him, no matter the emotion.
Later, the speaker says that the townspeople "laughed their cryings and did their dance." Unlike anyone and noone, the townspeople are discussed collectively and are not shown empathizing with one another's distinct emotions. Instead, they appear to share similar experiences and impersonal emotional responses. Indeed, parallelism equates this behavior to performing "their dance," suggesting that the townspeople all go through the same predetermined motions. Once again, the speaker utilizes antithesis to subtly tease out the differences in behavior among the loving couple and the members of their society.