Why does the speaker say that each person's singing "should be blithe and strong"?Walt Whitman's poem "I Hear America Singing"

The speaker says this because that is how he thinks the spirits of average Americans should be.  This is what he thinks the American soul is like.

In this poem, the speaker is talking about his vision of America.  It is a vision in which all sorts of regular (not elite) Americans are showing their spirits -- showing what kind of people they are.

Blithe means something like happy and carefree, lighthearted.  To the speaker, the typical American is like this.  The typical American feels free and lighthearted but is, at the same time, strong.