There are many theories about the development of children. By training, I presume that "upbringing" is inferred and whether the upbringing is affected by the mother's capacity and desire to breasfeed for any length of time.
Breastfeeding is like many other factors that affect upbringing. It is unlikely to cause any psychological harm by itself but if the mother failed to breastfeed because she could not bond with her baby or found it inconvenient, etc, it is not the breastfeeding, per se that will affect the child's "training" but the relationship with his or her mother.
It is possible that some mothers want to return to their previous routine, or as close to it as possible and they do not feel they have the time for breastfeeding; plus, they would have to be on-call or express breast milk on an ongoing basis - which some mothers have no inclination to do.
From a Health perspective, there are obvious and documented reasons why "breast is best" but, unfortunately, for some mothers it is not possible; similarly for adoptive mothers. In such cases, many mothers go out of their way to provide the reassuring environment created by breastfeeding by introducing their own nurturing environment.
When mothers return to work, especially in the modern era, many employers provide daycare facilities or access to such to allow a mother to be near her baby for bonding or feeding reasons. Shopping centers have special "feeding rooms" and breastfeeding is generally encouraged. It has become more about the whole scope of child-rearing than about any one aspect of it. Due to a better understanding
men and women have the time and resources to invest in their children
and recognize the importance, for fathers as much as mothers to be involved in their child's upbringing or "training." Many families and single parents, without sufficient support structures or facilities for breastfeeding, raise successful, contributing children despite the apparent hardships and difficulties associated with it so breastfeeding or not breastfeeding is unlikely to cause or contribute to poor "training."
More secure children who have developed positive patterns of attachment become secure adults, independent and able to form positive relationships. Even a recognition of the reasons why a secure attachment did not develop can also render well adjusted adults. These mothers recognize behaviors in their own babies and help their babies form secure attachments. Hence, the breastfeeding issue does not need to affect relationships nor the "training" of children.
It may be a sign of the times that breastfeeding is not necessarily popular due to the fast-paced lifestyle, young mothers who do not want to be inconvenienced by their children and a shortage of time to complete each day's tasks but that is the modern, selfish lifestyle NOT the modern, contemporary lifestyle.