This specific quote in Chinua Achebe’s Things Fall Apart comes at an interesting scene toward the end of Okonkwo’s time in exile in his motherland of Mbanta. Indeed, Okonkwo uses this proverb during a ceremonial breaking of the kola nut among his relatives from Mbanta:
“I beg you to accept this little kola.... It is not to pay you back for all you did for me in these seven years. A child cannot pay for its mother's milk. I have only called you together because it is good for kinsmen to meet” (166).
In this context, then, the quote does not mean that a child is not expected to pay for its mother’s milk, but rather that he could never repay the kindness that his mother’s clansmen have shown him. Earlier in the novel, they were gracious hosts and helped him out as he adjusted to life in Mbanta:
“Okonkwo was given a plot of ground on which to build his compound, and two or three pieces of land on which to farm during the coming planting season. With the help of his mother's kinsmen he built himself an obi and three huts for his wives” (129-130).
Thus, he is saying that the kola nut is not his attempt to pay his siblings back. Certainly, Okonkwo acknowledges that the way that they have helped him is invaluable. He cannot attach a monetary value to their help, and he potently compares their help to a mother nursing a child.