the speaker in birches compares the boy's climbing to

"swinging back and forth" on birch trees.

The speaker in "Birches" by Robert Frost compares the boy's climbing to "a boy bending them [the birch trees] to spray / freshet against the sun."

To answer this question, we need to analyze the poem "Birches" by Robert Frost.

First, let's establish the context of the poem. "Birches" describes the speaker's contemplation on life and the significance of imagination and memories. The speaker often reflects on his childhood experiences and the world of nature around him.

In the poem, the speaker makes a comparison between the activities of the boy climbing birch trees and the actions of ice storms. The speaker sees the bent birch trees, caused by ice storms, as resembling the boy's climbing, swinging, and descending motions.

To understand this comparison, we need to closely examine the lines from the poem. Here is an excerpt from "Birches":

"So was I once myself a swinger of birches. And so I dream of going back to be. It's when I'm weary of considerations, And life is too much like a pathless wood."

In these lines, the speaker mentions his own past experience of swinging on birch trees, implying that he too engaged in similar adventurous and carefree activities as the boy. The speaker longs to return to those moments of freedom and escape from the complexities of adult life, symbolized by the "pathless wood."

Later in the poem, the speaker further elaborates on his comparison:

"One could do worse than be a swinger of birches."

Here, the speaker implies that the boy's climbing of birches represents a kind of joy and innocence that can serve as a positive example. The boy's ability to climb and swing on the birch trees provides the speaker with a metaphor for living life freely and fearlessly.

In summary, the speaker in the poem "Birches" compares the boy's climbing of birch trees to the speaker's own memories of childhood adventures and the desire to return to a simpler, more carefree time in life. The climbing of birches represents a metaphorical freedom and resilience that the speaker admires and desires.