A child's soul comes from neither the father nor the mother. Each soul is created directly by God from nothing at the moment of conception. There is no pre-existence of the soul as Mormons and others believe.
The theory that the child's soul is an offshoot of the father's was held by some early Christian theologians. Augustine himself wavered between this position, known as generationism, and direct creation of the soul from nothing.
As theologians contemplated the teaching of Scripture and of the Tradition of the Church, they realized that generationism is incompatible with it. Thomas Aquinas went so far as to condemn generationism as heretical (Summa Theologiae I, 118, 2).