In “Birches,” why do the birch trees remind the speaker of childhood games?

"When I see birches bend to left and right

Across the lines of straighter darker trees,

I like to think some boy’s been swinging them.

But swinging doesn’t bend them down to stay

As ice storms do."

As you can see here in the opening lines of the poem, the birch trees remind the speaker of the childhood game of swinging on the branches of those same birch trees, or similar ones. It's because heavy ice from a storm has built up on the branches so much that they are actually bent downward, much like the speaker himself would bend those branches as a child when he played on them and his weight caused them to bend downward. However, the difference, as the speaker notes here, is that the ice has caused the branches to stay bent permanently, while when he played on the branches as a kid, the speaker only temporarily caused the branches to be bent.

This difference doesn't matter too much, though, because as soon as the poet has made that connection between ice-laden branches and his childhood adventures on similar trees, a bud of memories has appeared, and the poem unfurls from there. The speaker goes on to talk about how thrilling it was to leap from the trunk of the tree onto a branch, and he considers that activity in retrospect, with a thoughtful adult's ability to analyze that childhood activity and what it reveals about life.

You can understand this poem's structure, then, by noticing that it follows a common pattern: the speaker sees something, it reminds him of something from the past, and he goes on to juxtapose past and present and thereby discover new insights.