If you accept that SEP typically and in this case represents the academic state of the art and conventional usage, then look at the last section of the SEP article I linked to. It agrees with me (I think).
The SEP does not agree with you. No where in that section does it say that the "Why is murder wrong?" is a meta-ethical question. All it says is that while deontology does not assume a meta-ethical position, though certain meta-ethical positions are more hospitable to it. I agree with you and the SEP here.
I'm not saying deontology is a meta-ethical theory. It isn't. As I said:
And yes, deontology does not presume any particular metaethics. Your error, as far as I can tell, is in not getting what counts as a meta-ethical question and what doesn't. "Why is murder wrong?" is a straightforward question for normative theory.
By convention "why is murder wrong?" is a question for normative theory. Your sentence in the post, this one:
This is confused because the term ‘deontology’ in philosophical jargon picks out a normative ethical theory, while the question ‘why is it wrong to kill?’ is not a normative but a meta-ethical question.
is wrong. The SEP does not say otherwise. In any way. "Why is it wrong to kill?" is a normative question. Maybe what is tripping you up is this sentece from the SEP?
Likewise, a deontologist can claim that we know the content of deontological morality by direct intuition, by Kantian reflection on our normative situation, or by reaching reflective equilibrium between our particular moral judgments and the theories we construct to explain them (theories of intuitions).
I could see how that could be read as "reasons for the truth of deontological morality". But these are questions actually about the epistemology of moral claims-- "how do we know x is immoral?", is actually different from "why x is immoral?" Obviously these questions are usually connected but they don't have to be. It is logically possible to think that the Categorical Imperative makes murder wrong but that the way we learn that is by God speaking to us or by studying physics or whatever.
There's no sense in arguing about whether or not the distinction between normative and meta ethics reported in the SEP article makes sense. I agree that it does not. But we're not arguing about that. We're arguing about what the convention actually is.
The distinction makes plenty of sense. It just isn't what you think it is.
The SEP does not agree with you.
Great, I assume this means you think the SEP article is representing the convention. Let me know if that's not the case, since if it isn't, we're wasting our time talking about my interpretation of it.
Anyway, suppose someone were to come along and say 'Moral truths come primarily in the form of absolute injunctions!' (or whatever would fix him as a deontologist). We ask him for an example of such an injunction, and he says 'Do not kill.' So far, we agree that this whole discussion has taken place within normative ethics. ...
I think there’s a confusion in our discussions of deontology and consequentialism. I’m writing this post to try to clear up that confusion. First let me say that this post is not about any territorial facts. The issue here is how we use the philosophical terms of art ‘consequentialism’ and ‘deontology’.
The confusion is often stated thusly: “deontological theories are full of injunctions like ‘do not kill’, but they generally provide no (or no interesting) explanations for these injunctions.” There is of course an equivalently confused, though much less common, complaint about consequentialism.
This is confused because the term ‘deontology’ in philosophical jargon picks out a normative ethical theory, while the question ‘how do we know that it is wrong to kill?’ is not a normative but a meta-ethical question. Similarly, consequentialism contains in itself no explanation for why pleasure or utility are morally good, or why consequences should matter to morality at all. Nor does consequentialism/deontology make any claims about how we know moral facts (if there are any). That is also a meta-ethical question.
Some consequentialists and deontologists are also moral realists. Some are not. Some believe in divine commands, some are hedonists. Consequentialists and deontologists in practice always also subscribe to some meta-ethical theory which purports to explain the value of consequences or the source of injunctions. But consequentialism and deontology as such do not. In order to avoid strawmaning either the consequentialist or the deontologist, it’s important to either discuss the comprehensive views of particular ethicists, or to carefully leave aside meta-ethical issues.
This Stanford Encyclopedia of Philosophy article provides a helpful overview of the issues in the consequentialist-deontologist debate, and is careful to distinguish between ethical and meta-ethical concerns.
SEP article on Deontology