To clarify, we're using the colloquial definition, of involuntary sterilisation and "shower rooms". I've no objection to people getting together to voluntarily improve the gene pool.
As far as classic Ethics goes (Deontology vs Teleology), my general ethical position is an adaptation of Utilitarianism: greatest good for all. That is, each sentient being has infinite value. If it sounds like Deontology—it's not. If two people are tied on a track with a train coming, and you can pull a lever to switch it to a track with one person, ∞ + ∞ > ∞. Incidentally, I also disagree with Deontology, in that I believe inaction is an action.
I also believe life is greater than happiness. Call them different levels of infinity, say ℵ₀ and ℵ₁ if you like. So, Strict Utilitarianism says it's ok to kill someone if you provide enough happiness to enough other people, whatever that magic number is. I disagree, because ℵ₁ > n⋅ℵ₀ for any n. But you should still flip that train track, because ℵ₁ + ℵ₁ > ℵ₁ (by my prior declaration; I'm aware that isn't true in cardinal maths [let people be sets, if you like, so it's ordinal maths. People are complicated enough, I think]).
Thus, removing the immediate freedom and liberty of one person by sterilising or killing them, in order to theoretically improve the overall happiness of some number of future people, is wrong. ∴
Less traditionally, I really like Rawl's Theory of Justice. In a nutshell, one should act and make laws such that, if there were a birth lottery and you didn't know how you'd be born—black, white, rich, poor—you'd want to live in that world. So, you wouldn't want eugenics because you might end up born disabled or 'genetically inferior'.
To address jadedog's comment
That's circular. Value systems are not rational.
Value systems may or may not be rational, but my argument is not circular. If no value system is rational, then if one picks an arbitrary value system, and builds a rational ethical position based on it, their ethical framework itself is still rational. Which is important, because a great many people believe in ethical systems which aren't rational, and filled with cognitive dissonance.
If you believe no Ethics is rational, which it kind of sounds like, that's a different argument. Which I've countered before, and I'm not terribly interested in making again. Deconstructionism tires me. So we'll have to agree to disagree there, sorry.
Why value human life over other life?
Greater intelligence. Yes, intelligence is an arbitrary value. But it does seem to make life marginally less nasty, brutish, and short.