Does the church prohibit the artificial insemination of the wife with the sperm of her husband? If so, why, and how is this any different from any other medical procedure? If the love is there, and the desire to raise the child, and no adultery has occurred, where is the sin?
The response comes from the Cathechism of the Catholic Church.
2373 Sacred Scripture and the Church's traditional practice see in large families a sign of God's blessing and the parents' generosity.[162]
2374 Couples who discover that they are sterile suffer greatly. "What will you give me," asks Abraham of God, "for I continue childless?"[163] And Rachel cries to her husband Jacob, "Give me children, or I shall die!"[164]
2375 Research aimed at reducing human sterility is to be encouraged, on condition that it is placed "at the service of the human person, of his inalienable rights, and his true and integral good according to the design and will of God."[165]
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."[166]
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."[167] "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."[168]
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."[169]
2379 The Gospel shows that physical sterility is not an absolute evil. Spouses who still suffer from infertility after exhausting legitimate medical procedures should unite themselves with the Lord's Cross, the source of all spiritual fecundity. They can give expression to their generosity by adopting abandoned children or performing demanding services for others.
You can read the complete section on sexual relations at this link.