If a pro-choice person you're talking to understands the distinction between the question of biological humanity and philosophical personhood, he/she will undoubtedly attempt to find some property/properties that persons must possess in order to be a person. Some common ones are consciousness, self-awareness, sentience (meaning the ability to sense and feel pain), and desires.
While the person is attempting to locate personhood grounded in these properties, they will usually support their criteria by arguing from analogy. Rocks are not conscious things, and it is not wrong to destroy rocks. The unborn are not conscious, so it is not wrong to destroy the unborn. This can be a common comparison, such as one being made by this individual whose article I came across. Even professional philosophers engage in these kinds of comparisons, although unlike those at the popular level they make a better comparison. They don't compare the unborn to inanimate objects like rocks, but will compare them to other living things, such as when Mary Anne Warren, in her essay On the Legal and Moral Status Of Abortion, argues that the unborn, in the relevant respects of consciousness, are less personlike than the average fish.
The problem with this argument is that it commits a lesser known logical fallacy called the category error fallacy (or category mistake). A category error is a semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category.* For example, the statement "the number seven smells like pine trees" is a category mistake because numbers are abstract objects and don't produce odors.
What's the category error being made here? By comparing unborn human embryos/fetuses to objects like rocks or living things which do not possess consciousness in the relevant sense to have personhood attributed to them, these pro-choice people are attributing the category of non-consciousness to the unborn human embryo/fetus, when in fact the unborn are not non-conscious, they are pre-conscious. This is an important difference. It is not wrong to destroy rocks because they are not the kind of thing which has a serious right to life. Nor are fish the kind of thing that has a serious right to life (and if they were, it would be just as wrong to kill immature fish as it is to kill mature ones). Your intrinsic value and rights depend on the kind of thing that you are. Since the unborn belong to a conscious species and they are self-directed entities who will develop the present capacity for consciousness if not prevented from doing so, they are in a different category than rocks and guppies.
So whether or not the active potential to develop along the path of human development is morally relevant to the unborn human's intrinsic value (as I argue it is), comparing unborn human beings to non-conscious entities does not do the work of arguing against it.
*Simon Blackburn, The Oxford Dictionary of Philosophy, Oxford University Press, 1994, p. 58.