Child rearing is a big responsibilty shared by both the parents however, when it comes to equality i personally think that mothers are more responsible for raising a child as compare to a father as children are more influenced by their mother and it is her duty to up bring a well disciplined child now that does not at all means that a father is no longer responsible for child rearing , he too has some responsibilties of course while a mother can more rise a child as their is a unique bond between a mother and a child since birth.
A mother can be responsible to teach manners how to eat, sleep and different behaviors as there is much interaction of a child probably an infant with his or her mother while a father could be out at job working hard the whole day might not have time to spend with his family. Therefore, its basically a mother's responsibilty to look after a child during which a child learns alot from a mother.
Moreover, a mother is more careful and sensitive in rearing a child as there is a unique love and affection in this relation of mother and child which might not be seen in a father-child relation. A father and child relation can be a bit complicated as there is seen in some cases that a father can be strict in raising a child due to which a child can be too aggressive or too shy depending upon the varying nature of every child. That is why mostly children are more close to their mothers as they know that if anything goes wrong a mother can always find solutions to their problems.
Thus, it is the responsibilty of both parents to rear their children into better human beings. However, this is more important for a mother to spend time with children and raise them in such way that enable them to prosper in their lives.While a father is more responsible to fulfill their financial needs and also give them his best time as much possible. Therefore, A mother is more responsible in child rearing as mother - child bond is more strong and influential in raising a child.