Now and then I encounter the simplistic claim that destroying human embryos is murder because, well, they're human. I hardly know where to start in rebutting this, since it is so muddled, but I think it's worth repeating the basic points here.
Nobody can deny that a human embryo is "human" in the sense of having DNA belonging to the species Homo sapiens sapiens. Those of us who support biomedical research on human embryos are, of course, well aware of this - but it's not what the argument is about. When we deny that destroying human embryos is murder, we are denying various other things. In particular, we deny that human embryos have such characteristics as sentience, rationality, self-consciousness, and moral autonomy (the ability to reflect about decisions and life plans). We deny that they are yet part of any community into which they have been born. In these ways, embryos are very different from human adults, children, or babies. They are not the kind of thing that fears death, or that we can feel sorry for (they can't suffer, feel grief, be maddened by frustration, or have their life plans fall into ruin); they are not beings whose killing disturbs the peace within our societies or typically causes severe parental grief, as does killing someone's precious baby.
The law relating to murder, along with the moral baggage that goes with it, does not relate to the killing of just any living entity that belongs genetically to the species Homo sapiens sapiens. It's worth bearing in mind that abortion has never been considered murder at common law. The law of murder is about keeping the peace and protecting us from things we rationally fear - threats to our lives or the lives of loved ones - rather than about conserving entities with particular DNA sequences.
A good way to understand this is to do a thought experiment and consider the position of a sentient, intelligent, self-conscious alien that has become part of our community. Presumably if someone maliciously killed this being, that would be murder. Similarly, if someone maliciously killed one of the mutants in the X-Men media franchise, we would (as readers or viewers) interpret it as murder even though these beings supposedly have different DNA. If we lived in a community made up of more than one kind of intelligent species, killing individuals of either, or any, of these species would breach the peace, arouse our fears for our own lives, etc., and would have to be considered by the law to be an act of murder. In short it is not DNA-based species membership that matters, but something's actual properties (such as sentience, rationality, etc.) and social relationships.
Note that I don't have an overarching theory that says it is just one thing or factor that matters morally - perhaps personhood. I am happy to accept that personhood is neither a necessary nor a sufficient condition for something to be a potential murder victim, even though it is an important matter for consideration by legislators. I can readily imagine that there might be a species of malevolent, or just totally alien, beings who possess the characteristics we call personhood (e.g. rationality and self-consciousness), but have no propensity whatsoever to bond into communities with humans. They may be so radically different from us that their entry into the same social contract is out of the question. Killing such a being may be a matter of great regret, and may even be something that we have a moral reason not to do, but I don't necessarily want to count it as murder or expect the law to classify it as such.
On the other hand, newborn human babies are not yet persons, but we have good reason to view their killing as a very serious crime, at least in normal circumstances (forget cases of anencephaly, severe disability and so on). We bond and empathise with babies instinctively; they are typically immensely loved and valued by their families; they carry many of our hopes for the future. Whether we classify infanticide (in ordinary circumstances) as a sub-set of the crime of murder, or as a sui generis crime, is largely a matter of social convention. But categorising it as murder makes perfectly good sense as an option available to society as it develops its code of criminal law.
I actually have a very pluralistic view of what factors underpin our moral and legal systems. To the extent that we are tempted to think there must be just one single factor on which morality depends, that is one of the errors about the phenomenon of morality that it is easy to fall into. However, I can see no factor that compels us to treat the destruction of human embryos as a serious moral wrong of any kind. At most, the symbolic significance they have for many people, perhaps including ourselves, may make us feel the need to adopt a degree of solemnity whenever human embyros are destroyed, and to look with disapproval on anyone who treats such processes flippantly. This is analogous to the sensitivity and respect that we show in the presence of a corpse, but it is long way from the considerations involved in applying the concept of murder.
Often, when I make these points, I feel I'm bashing my head against the proverbial brick wall. One might think that, by now, such points would not need to be made yet again - and again, and again, and again. However, that is evidently not so. Yes, these points still need to be made, so here they are once again, at least for the record.