I agree with joycew. Cora knows that she, and the other adults who come to the farm from slavery, can never fully shake the trauma. Much as they may cherish their freedom, they can't fully live into it. But the children who have only known freedom would not carry that burden, and if their freedom wasn't challenged or undermined by white people -- a big if -- they could follow their dreams and never know how much it saps one's spirit and hope, for a human being to be seen, thought of, and treated like an animal, or a disposable piece of property, or simply as an enemy, judged as a threat or a failure on sight alone (like today; a white man's fear and loathing can get you shot like Trayvon Martin).
Cora knows this, but Whitehead knows that most white Americans do not realize it, and that is what makes this quote, and this novel, full of impact for today. Through Cora he is trying to help us recognize our own white privilege. For most whites, we do not have to live in this constant fear and see our children's joy and hopes crushed just because they are born white.