This is a very long question; I think the sheer length of it makes it a bit overwhelming to answer, so let us try to break it down. What you are actually being asked is the following:
1. What is the theme in Housman's poem "To an Athlete Dying Young"?
2. What is your response to this theme—do you believe that dying young confers a sort of eternal life, and is this really a good thing? Does Housman really believe it? What are the pros and cons of the argument?
Looking at the poem itself, then, the theme seems to be, as the phrasing of the question suggests, that even the greatest of athletes who was lifted "shoulder high" in his youth will find that "glory does not stay." Only by dying young can the "early-laurelled head" draw crowds to gaze upon him in his coffin; the "garland" of his youthful brilliance and athleticism is "briefer than a girl's," presumably indicating that his youthful prowess will "wither" even sooner than a young girl's beauty.
The real question to ask here, though, is what Housman's attitude is toward this situation. Does he really mean to suggest that it is "smart" to die young in order to maintain the glory of youth? Alternatively, is he critiquing the society in which those who are vaunted football players as teenage boys in small towns go on to feel that their life is a downhill slope from that point? Does the passage of the athletic prowess that marked them out in youth make them feel unremarkable in its wake?
In responding to Housman's theme, think about how it makes you feel. Do you think it is true that fame and glory is maintained the longest in those who die young? There are certainly many people whose lives seem to bear out this thesis—you might discuss some, such as John F. Kennedy, Martin Luther King, Elvis Presley, Buddy Holly, and so on. But doesn't Housman's poem seem to be mourning a particular kind of youthful energy in young men—the specific joy of being an athlete? What happens to athletes in our society? It is true that their careers in sports are often brief. But what happens after their football season is over? In many instances, they go on to have rewarding careers as commentators and writers while still being remembered for their early prowess.
You could also widen the question to consider other fields. For many, it takes a long time for them to reach their peak. Many famous actors, like Harrison Ford for example, did not even become recognized until they were in their thirties. Many scientists and writers took even longer to get their careers off the ground, so it cannot be said that all of our glory lies in our youth. Maybe some of these people were youthful athletes who mourned when they became unremarkable in that sense—only to discover a second great talent later in life.
Consider how specifically you think Housman is speaking to youthful athleticism in this poem. I would argue that he is talking quite particularly about this type of youthful glory because he defines it as so brief—even more brief than that of a girl's beauty. In most ways, it is indeed the case that this type of glory is very fleeting, and in some cases, it marks the absolute pinnacle of people's lives: their heads are "early-laurelled" while the rest of their lives are a disappointment. But doesn't this depend on the individual as to how they allow the passage of this talent to make them feel? Do you think that people should accept that early glory is brief and that early death is the only way to keep it alive, or is there an opportunity to prove oneself by showing strength and aptitude in other ways?