1. The Humanity argument: First, one might appeal to the idea that individuals inherit a baseline moral status just in virtue of the kind of being that they are -- in technical terms: what matters is the substance, and not just the phase, sortal. (So, for example, even severely retarded humans still have rights in virtue of being human.) But embryos are human individuals too -- that's a biological fact. So embryos have the basic rights / moral status that go along with this.
There are two things to note when charitably interpreting this argument. Firstly, it does not imply that any old human cells (e.g. fingernail clippings) have moral significance, as critics commonly assert. Moral status is here only attributed to whole organisms, and a human fingernail is not a human organism, or 'individual human life', the way that a human embryo is. Secondly, it isn't a purely biological notion of 'humanity' that we're working with, because non-conscious zombies would be biologically human organisms, yet few think that they matter morally in the way that conscious persons do. So the relevant 'kind' here should really be understood as something more like 'sentient, rational animal' (SRA). Then the argument runs as follows: SRAs matter morally; embryos are (merely an immature, underdeveloped phase of) SRAs; hence embryos matter morally.
The problem with this view is that it runs afoul of our 'end of life' moral intuitions. Irreversible loss of conscious surely marks the end of the person's existence (in any morally significant sense). But the human organism (SRA) might live on, on life support, while in a (permanently) non-sentient 'phase'. Does anyone really want to say that this permanently non-sentient body retains a 'right to life'?
2. The Deprivation / 'Future Like Ours' argument. Marquis gets around this problem by saying that what matters to the morality of killing is not one's general 'kind', but rather your individual future (that death would deprive you of). The brain-dead patient has no future to look forward to, which is why biological death does no further harm to them. But an embryo has a whole lifetime's worth of experiences that death would deprive it of. So embryonic death is a most grievous harm.
The problem with this argument is that there's no good reason to think that the embryo would be the subject of the future experiences anyhow. That is, it presupposes the (clearly false) bodily conception of personal identity. As I put the argument in a previous post:
If a mad scientist scanned my brain, disintegrated my body, and then wiped your brain and implanted all of my mental traits (memories, beliefs, values, personality, etc.) in its place, then it seems that I have gotten the better half of the deal. I have survived and you have not. Though your body is the one that lives on, it is our minds that matter, and it seems that your mind has been replaced by mine. In making this judgment, we implicitly judge that it is the content of a mind that matters -- the memories, beliefs, desires, and so forth -- not its "location" in a particular body, or even a particular brain.
Suppose this scenario goes ahead. I awake in your body and return to my old life (as best I can). Does this make any difference to you? Suppose you're told beforehand that after your mind is wiped and replaced with mine, I'll go on to live a happy life. Or maybe you're told that I'll be killed the next day. You might for altruistic reasons prefer the former news, but do you think that you are harmed if the latter outcome occurs instead? If not, this goes to show that preventing future pleasures from being experienced in your body is no harm to you, if you are not the one who will get to experience them.
Any kind of psychological view of personal identity (or what matters in survival) straightforwardly implies that mindless embryos do not "survive" in the morally relevant sense. So they never had any 'future like ours' of which they could be deprived. In other words: since they will not be the ones to experience the future life in any case, it is no harm to them if that possible future life is prevented by means of abortion.