In my opinion, it is a responsibility of parent to bring up a child morally, as they bring up a child from the birth and only they can educate him or her morally as we know children should be brought up till three years old and they gave their own character.
Only parents know their children well, it is up to the family to bring up moral education, it is the task of the family to teach some life standarts for children because moral values can be given in the family from generation to generation
That may be so but the parent's can't teach their kids everything they need to know, unless they want their children to be in the same career as them. In that case we would have no need for teachers because then kids would be born into their parents' jobs. Those who were born to be a teacher would have no job because there would be no need for it. We have teachers to teach our kids so they can choose their own careers and make their own future, instead of living a dull life.