Read "To an Athlete Dying Young" aloud and you'll realize pretty quickly that sound is a major player in this one.
First off, there is a kind of galloping rhythm (for more on what's causing that galloping check out "Form and Meter") that brings to mind the regular footfall rhythm of running. In this sense, the poem's rhythm mirrors the content: the poem is about a runner and it feels like running. (True. It's about a dead runner, but work with us here).
In addition to sounding runner-y, it also sounds a little singsong-y. That's due to all that strong end-rhyme and heavy doses of alliteration and consonance. For example, check out all the repeated S sounds in line 15, both at the beginning of words (alliteration) and throughout (consonance):
And silence sounds no worse than cheers
What we end up with is a poem that sounds like a nursery rhyme but with very grown-up content (the fleeting, fragile nature of life and fame). We don't really expect this kind of content with this kind of sound. Poems that sound this bouncy and song-like should be about puppies and friendly dragons.
The disparity between the sound and the content mirrors the great contrast between youth and death. These things don't belong together. And Housman doesn't just give us any old youth (old youth, get it?). He gives us a healthy, vigorous, victorious youth—and he's dead. It just isn't right, right?
The poem's youthful, bouncy sound also mirrors the idea that, as the speaker suggests, there are lots of benefits to dying young: the athlete goes out on top and will always be remembered at the height of his athletic prowess. Even though the athlete is dead, he'll be remembered as vital and victorious; even though the poem is about death, it sounds alive, bouncy, youthful.
What we end up with is a poem with a very controlled, familiar, comfortable sound about a very uncontrolled, uncomfortable subject. Perhaps Housman was trying to use sound to make the athlete's death a little easier to consider, a little less terrible and tragic.