Of course, any work of poetry opens itself up to a number of different meanings, and it is very hard to pin down any one definitive explanation of such a diverse medium. However, here is my "take" on this excellent poem.
In this poem, Hughes seems to be talking about the way that society treats the "genius child" with suspicion and fear. The way that the genius child is related and compared to an eagle or a monster suggests that there is something in the intelligence and capacity of a genius to change society that threatens society. This of course results in a real fear of the "genius child" and the way in which he is unloved. A genius child, through his talent and intelligence, threatens the status quo by offering the potential for change. The song of the genius child is "wild" and unpredictable, because change always involves a venture into the unknown. That is why the song must be sung gently, so that it does not "get out of hand":
This is a song for the genius child.
Sing it softly, for the song is wild.
Sing it softly as ever you can -
Lest the song get out of hand.
The series of rhetorical questions seem to argue the danger that is implicit in a genius child, ultimately comparing such a child to a "monster / Of frightening name." The final, shocking line seems to present the attitude of society towards such genius children who offer so much hope and potential for meaningful change:
Kill him - and let his soul run wild.
Far better to extinguish such children and let the status quo remain, so that we can maintain control and predictability in an uncertain world. Obviously, Hughes does not believe this, rather he uses the poem to capture the attitude of society towards innovation and those that try to usher such changes in. Many, through their suspicion against new ideas, would commit violence to maintain stability.