Kerouac chose Whitman because...

Whitman cherished his ability to open himself up to others. He expressed such beliefs through poetry, and now we see Kerouac using a similar medium to do the same. Kerouac is recounting his time on the road with brutal honesty and surrender to the reader.
Whitman's quote perfectly introduces the book as an invitation to the reader. It encourages them to immerse themselves in the book, becoming equally as vulnerable as Kerouac was while writing it.