Here is my outline of the argument in Warren's essay "On the Moral and Legal Status of Abortion"

Warren asks, "What does 'human' mean?"

People tend to assume that "human" means "genetically human." Let us designate that sense as human_G. Warren is interested in a more Kantian definition of "human" – "human" in the moral sense (human_M). Kant includes angels, God, and other non-human rational beings (if they exist) as human_M although they are not human_G. Being human_M implies (1) that one is a member of the moral community (i.e., one is bound by the commands of morality); and (2) that one possesses the rights and duties accompanying such membership.

Warren argues that the word "person" should designate only human_M.

Being human_G is neither necessary nor sufficient for being human_M; some humans_G are not humans_M (e.g., infants, severely retarded people) and some humans_M are not humans_G (e.g., intelligent ETs, angels, etc., if they exist). None of this is controversial in philosophy.

On the standard view of rights (e.g., the right not to be killed, aka the right to life), only creatures with duties have rights. That is, I acquire a right as a consequence of the fact that I am a being capable of acting from duty – in other words, as a consequence of being a member of the moral community. Creatures with no possible duties have no rights. This is why, on the standard view, non-human animals are thought not to have rights. It’s because they are thought to have no duties. Some animal trainers (e.g., Vicki Hearne, author of Adam's Task) would dispute this.

Warren’s argument is quite simple, then. It’s clear that as long as a fetus is a fetus, it has no possible duties and is thus not a member of the moral community. Fetuses are human_G only; they are not human_M. Because "person" means human_M, fetuses are not persons. Thus, according to Warren, they have no right to life and abortion is always permissible. Only humans_M ("persons") have the so-called right to life (i.e., the right not to be killed – except, perhaps, for a very good reason).

Warren proposes a thought experiment involving an imaginary space traveler having to decide if alien beings should be considered humans_M, and thus have the right to be respected as ends in themselves, the right to life, the right not to be eaten, etc. (Friend or food?) Warren says if we encountered beings with all the following characteristics, we’d consider them human_M:

1. Consciousness and the capacity to feel pain
2. Open-ended reasoning ability
3. Self-motivated activity
4. The capacity to communicate in an open-ended way
5. Self-awareness

Warren says perhaps some of these characteristics are more essential than others. The point is, however, that a being lacking all five couldn’t possibly be human_M, and having (1) alone (like a fetus) is not sufficient.

1. A more highly-developed fetus is "not significantly more personlike than is a very small embryo," so we should not think late-term abortion (at 7, 8, or even 9 months) is more evil than very early abortion. "…[I]n the relevant respects, a fetus, even a fully developed one, is considerably less personlike than is the average mature mammal, indeed the average fish."
2. The fact that a fetus is a potential human_M is relevant but does not override the right of the woman to an abortion because the rights of an actual human_M (person) always outweigh the rights of a potential human_M (person). As Warren’s example of the space explorer (who can choose to be cloned) illustrates, the rights of a single actual human_M even outweigh the rights of millions of potential humans_M.