The answers you have been given are accurate, but not comprehensive. This link is to the instruction which covers the issues in detail.
I think two things are hard for us Catholics to convey. One is that we hold human life to have very great intrinsic dignity. And the other is that we think, hold onto your hats, things are what they are.
From the first arises the idea that the means whereby which God has ordained that humans are ‘made’ also have very great dignity. The two people engaged in baby-making are themselves creatures of dignity, and the action can provide the locus where God repeats the wonder of creating a “rational soul,” and therefore has very great dignity.
Further, because humans are not a body + a soul but one “ensouled” creature, their proper actions are done with both will and body involved. So intimate an activity as sexual intercourse properly involves a commitment of will as intense and intimate as the commitment of bodies. Thus the essential problem with fornication is that it rends body from will and fragments the human being.
Therefore, even if no embryos were killed and if semen could be acquired without masturbation, IVF would be wrong because of a similar rending.
This may be hard to grasp because we have cheapened sex. But when we fell in love, and when we “made love” at least once we recognized the miracle that we can breed like sheep, but with a great deal more enjoyment than they seem to have, AND we can “mean it” in a way they never could.
As to the second. What I mean by “things are what they are” is sort of like this. When we read that the wealthy Romans at their banquets made themselves vomit so they we could eat more we think not only of the piercing smell of vomit or the pathos of the starving poor, but of the perversion of separating the pleasure of conviviality from nutrition. And we recognize that even if we could supply healthy nutrition by the means of IV drips and NG tubes, the “plene esse” of nutrition for humans is to eat and drink, optimally with friends.
Similarly, we have little difficulty saying that the heart is “for” circulation. If we could somehow separate circulation from the other functions of the heart (I can't think of any) we'd still say it “just ain't right.”
So, if I've established at least the idea (whether you agree with it or not) that sexual intercourse is imbued, we might even say “demands”, a very great dignity
AND IF I have sketched the notion of things being what they are so that the “plene esse” of intercourse is a new human miracle,
THEN I think I have sketched a ‘system’ in which it would be wrong to separate procreation from intercourse.
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