You have a hard road here because in the end refusal to acknowledge the wrongness of artificial insemination is a problem of the will, not the intellect.
Let’s summarize what makes it so difficult:
–The good intentions of the couple. Children are naturally and normally an outgrowth of true marriages and it is right that couples want and expect them.
–Modern sense of entitlement. The false doctrine of “reproductive freedom” as a two-edged sword. On the one hand used as a justification for reaching into a person’s womb with a pair of forceps and dismembering the innocent human within. On the other hand used to invent a “right to a child” with the implication of “by any means available”, which is part of:
–modern Man fully indoctrinated in consequentialism, or the belief that the ends justifies the means.
–The domination of Man by technology and a near obliviousness to how often it is actually enslaving us rather than helping us.
That’s a lot of jungle to cut through to Truth and clarity. But, for what it’s worth, I think one can put the Catechism into layman’s terms and hope and pray that those with ears hear:
2376 Techniques that entail the dissociation of husband and wife, by the intrusion of a person other than the couple (donation of sperm or ovum, surrogate uterus), are gravely immoral. These techniques (heterologous artificial insemination and fertilization) infringe the child’s right to be born of a father and mother known to him and bound to each other by marriage. They betray the spouses’ "right to become a father and a mother only through each other."167
2377 Techniques involving only the married couple (homologous artificial insemination and fertilization) are perhaps less reprehensible, yet remain morally unacceptable. They dissociate the sexual act from the procreative act. The act which brings the child into existence is no longer an act by which two persons give themselves to one another, but one that "entrusts the life and identity of the embryo into the power of doctors and biologists and establishes the domination of technology over the origin and destiny of the human person. Such a relationship of domination is in itself contrary to the dignity and equality that must be common to parents and children."168 "Under the moral aspect procreation is deprived of its proper perfection when it is not willed as the fruit of the conjugal act, that is to say, of the specific act of the spouses’ union . . . . Only respect for the link between the meanings of the conjugal act and respect for the unity of the human being make possible procreation in conformity with the dignity of the person."169
2378 A child is not something owed to one, but is a gift. The “supreme gift of marriage” is a human person. A child may not be considered a piece of property, an idea to which an alleged “right to a child” would lead. In this area, only the child possesses genuine rights: the right “to be the fruit of the specific act of the conjugal love of his parents,” and "the right to be respected as a person from the moment of his conception."170