You have asked for some examples of mothers who failed to put their children first and why. Beauvoir argues that to be a good mother and to genuinely put the needs of her child first, a woman needs to have an independent sense of her own self-worth. Not all mothers are good mothers as many use their children to fulfill their own needs. As Beauvoir explains:
Mystification begins when the religion of Motherhood proclaims that all mothers are exemplary. For maternal devotion can be experienced in perfect authenticity; but in fact, this is rarely the case. Ordinarily, maternity is a strange compromise of narcissism, altruism, dream, sincerity, bad faith, devotion, and cynicism. (632)
Some examples of mothers who fall short, a falling short that derives from the woman's sense of inferiority to men, are the following:
Beauvoir cites Violette LeDuc's In the Prison of Her Skin, in which a woman beats her daughter because she, the mother, was humiliated and angered when abandoned by her seducer.
Beauvoir cites psychologist Helene Deutsch's story of a woman, Mrs. Mazzetti, who, feeling thwarted herself, both pushed her children too hard and monitored her children too strictly, oscillating between love and hostility, until they all rebelled.
In a third instance, Beauvoir cites Freud as she describes the masochistic mother finding fulfillment through a son that she wants to be "hers." This leads her to encourage his dependence by encouraging him to be selfish, shy, sedentary and greedy. With a daughter, this type of mother will project all her doubts about her self-worth onto the girl under her control. Sometimes she will heap the worst chores on this child or strike her because of her own-self hatred and/or hatred and resentment of her husband.
In the end, a woman needs to feel autonomous and good about herself to be a good mother. It is unhealthy for children to be "the full horizon" of a woman's expectations: she needs a fulfilling life of her own, says Beauvoir.