I would suggest a couple reasons. Perhaps the most obvious is the form. Song of Myself is written in a new and unique type of free verse, in some ways closer to the cadence of the human voice that the written word; in fact, I have always found the poem very difficult to read, but much easier to read aloud and enjoy the unique rythm of his language. It is also full of his endless lists, lists of almost everything treated in a way that they all seem to be equal in the end. This is the other thing that makes the poem so special. It is the first truly American poem (although I suspect arguments could be made for others). Emerson pleaded for an original literature for America, a literature worth of the vastness of America and its dreams; many of these are contained in his essay, "The Poet." When he first read Whitman, he recognized him as the poet he sought:
I am not blind to the worth of the wonderful gift of "LEAVES OF GRASS." I find it the most extraordinary piece of wit and wisdom that America has yet contributed. I am very happy in reading it, as great power makes us happy. (Letter from Emerson to Whitman).
The other reason is that Whitman is the great poet of democracy and has an almost mystical sense of the union of all things. He writes of working men and prostitues, slaves and freeman, and all of them are part of him and his great lists. In his poetry we find the celebration of the great hope of the American Experiement.
And I know that the spirit of God is the eldest brother of my own, And that all the men ever born are also my brothers . . . . and the women my sisters
This is the meal pleasantly set . . . . this is the meat and drink for natural hunger, It is for the wicked just the same as the righteous . . . . I make appointments with all, I will not have a single person slighted or left away, The keptwoman and sponger and thief are hereby invited . . . . the heavy-lipped slave
is invited . . . . the venerealee is invited,
There shall be no difference between them and the rest
And that a kelson of the creation is love;
This was the beginning of a truly American Literature ... in subject and technique. It's not always easy to read, and it's not equally great, but it was clearly the beginning.