A farmer's heart is rabbit soft,
And farmer eyes are blue.
But farmers' eyes are eagle fierce
And look a man right through.
This little poem captures the odd combination of down-to-earth get-it-doneness and kind-heartedness that we see in Papa and, by extension, in all people who live off the land. Notice the way the poem uses concrete imagery from nature ("rabbit soft," "eagle fierce") to express the contradictions (vulnerability/determination, soft-hearted/fierce-eyed) that are just naturally part of a life like Papa's. Although Papa can cry without shame at Pinky's death, he knows that he has to face up to the harsh realities of his life and be "eagle-fierce" when it's called for.
All in all, the epigraph seems to celebrate the way that farmers, and other people who live close to nature, bring together seemingly opposite qualities and make 'em work.