what type of fallacy is this?

I would suggest it is a red herring. Choosing a house, school, surgeon, or car is not similar to the ethics of eugenics.

It looks like a fallacy of equivocation. It's a bit like saying "I am complimented on my discriminating tastes in food and clothes, so why am I criticized for discriminating against blacks?" Here, the equivocal term is "choose," since it has different meanings in the context of choosing, e.g., a school and choosing a baby.

I dont think this involves a "fallacy of equivocation", only the ethical argument of whether such choice should be exercised.

http://www.actionbioscience.org/biotech/agar.html

I agree with Joe; "choosing" has different meanings. "Choosing" a school or a doctor means selecting from different opportunities. "Choosing" a baby means performing experimention on humans with limited understanding of the impact.

http://www.fallacyfiles.org/equivoqu.html

It isn't a fallacy at all. There's nothing wrong with wanting to have the best baby possible.

Not considering the merits of baby trait selection, it is a logical fallacy to compare "choosing" a baby to "choosing" a doctor. Apples and Oranges.

The desire to have the best baby possible is not fallacious reasoning, but the argument, which relies on the equivocal meaning of "choose," is fallacious.

Or it could be an implicit assertion that the two are the same.

And why wouldn't one assert that? The embryos that picky parents would be likely to select between are very early ones. Current American law accords no legal rights to them, and most leading schools of ethics, no moral rights. Therefore, choosing one embro over another quite arguably is equivalent to choosing one movie over another.

I'm prepared to meet you half-way though: If the above statement was a fallacy, it would be that of equivocation. Deal?

Deal.

It seems to me that the status of "choice" being disputed depends on the current state of genetic engineering. On the assumption that "designer babies" will ultimately be a viable proposition I can see no reason why "choice" should take on a different characteristic to the normal usage. Where I can see a dispute is over the word "best". The nub of the dispute seems to be whether we see human breeding as similar or different to animal breeding over which we already excerise "choice".