I'll take a stab at it. There isn't ONE reason why I feel this way, it's more of a collection of thoughts and running into some pretty interesting tidbits over the years that I don't really think it's a good idea.
But first I worry about the health of the mother. Hormones are not something to mess around with. I don't think there is anything in the lit. that proves causation of anything, but when you're doing things to women from so many backgrounds and there are a thousand things that can happen, some within years, some take decades to show up, and the results can very so wildly it would be rather hard to prove or disprove any of it anyway. some never have anything happen other than happy healthy children.
They shown that simple diet changes have genetic impacts generations down the line. There were some rather interesting findings from studying descendants from the Irish potato famine. What do these treatments do 2-3 generations down the line? So far they say nothing, but do we really know? Can we really understand the ramifications? Short term I think we can, but we're not very good at looking too far into the future.
I wonder about the development of the child. I know they appear to be normal in everyway for the most part. I'm not aware of anything that seems to "run" in AI babies as they grow, but what's happening 2-3 generations down? or what will happen? Smoking and drinking are harmful, artificially manipulating hormones and using other meds can also have a profound impact on any development as well. It's hardly a stretch to think so.
And it's just a basic life philosophy that nature is not usually "wrong". I know dogs were brought up earlier as a comparison and my feelings are that at some point we will ruin most breeds and we will have to start "over" by allowing things to happen a bit more naturally for a while. Our selective breeding for animals is good for our own short term wants, but I don't think it's good for the overall health of the species. How do I prove it? I don't know, i think there's enough out there staring us in the faces on that topic, but if others don't see it, I guess I don't care either. I still look for dogs from a breeder
rather than some bush dog from Australia.
I think once humans start doing that on any more than a research type scale, we're screwed. It's one thing to artificially manipulate conditions so a fetus can be brought to term, and quite another to manipulate that and then the genome. We know very little about genetics and how everything meshes. Things we do now will have rather large impacts down the road. When we select for certain things, other things always creep up. Temple Grandin's story of the "raping roosters" comes to mind. we see those things in animals because they breed more often, but in humans, some of this stuff won't be visible for 100 years or more and when it's done on a small scale, it might take even longer before these changes get "paired" up thru mating down the road to show us anything if there's anything to be seen.
I'm not going to begrudge someone that choses to do fertility treatments to have a baby. I don't think it's a good idea, it's why we haven't done it. I do stand against specifically selecting genes and making test tube babies. I don't care if it's to "avoid" a genetic condition or not. Our success ratio at predicting such conditions isn't exactly great, though many think it's almost an exact science.