When we ascribe personhood to an individual or category of individuals, this is ultimately based on arbitrary metaphysical assumptions about which it is pointless to argue. What we can do is discuss the practical, real world ramifications of the ascription or denial of personhood in particular cases. Even then, we will ultimately bump against subjective value judgments about costs and benefits and priorities, but it is nonetheless useful to get past the stage of "x is a person" versus "no it isn't" and to engage in constructive dialogue.
Suppose that I adhere to the irrational normative proposition that all spermatazoa are "persons" entitled to the rights and privileges apputenant thereto. After all, given access to an egg and a womb and just the right conditions, the sperm could become a human. This implies that I might support measures, however inconvenient or costly or draconian, to prevent the mistreatment or unnatural death of sperm. What do we gain by ascribing personhood to sperm? Nothing other than the satisfaction of appeasing me and my ilk in the "masturbation is murder" movement. In fact, we take on an onerous burden with no objective payoff for the social order. After all, sperm can't reciprocate. I don't deal with sperm in any manner that resembles my dealings with other "persons". Sperm don't respect my rights or personhood, and they can't even violate them of their own volition. Ascribing personhood to them seems ridiculous for these reasons and because of the difficulty of enforcing spermatazoa rights.
One might make the same arguments about human egg cells. What's the point of making them persons and recognizing rights? It is possible that a proponent of ova rights would use the ova as person argument as a justfication for the consequences of such a stance. It might suit the advocate of ova rights to limit the movement and freedom of women and to maintain an intrusive surveillance apparatus for reasons utterly unrelated to ova with ova rights being a tool to bring unwitting dupes on board with his program. Otherwise, nothing is to be gained by recognizing ova as persons.
The same goes, I reckon for an ova which has been fertilized by a spermatazoa. The fertilized egg is in no better position to recognize my rights or to violate them or to reciprocate with me in any way than the sperm or the egg that it once was. Affording it personhood does nothing other than diminish human freedom with no payoff other than appeasement of the subjective, irrational beliefs of a portion of the population. Those who call the fertilized egg a person must expect consequences to flow from the ascription, and it is likely that many who do so understand their position as a means to obtain mass support for the application of measures which protect fertilzed eggs at the expense of actual sentient human beings.
Suppose the egg successfully plants itself in the uterine wall. Nothing has changed really for the purpose of our analysis. Nothing is gained by calling it a person, and a big burden is shifted onto actual sentient human beings. The cell divides and begins to differentiate, and all along the way it remains incapable of respecting another human or reciprocating with us in any way.
At some point, protecting the fetus becomes sufficiently less costly and inconvenient that it begins to make sense to offer it some legal protection. It is not necessary to characterize it as a person in order to do this. And the interests of the actual sentient human being who carries the fetus should certainly weigh heavily and take precedence in most cases.
Let's not get caught up in whether a fetus is a person. Let's just decide what protections a fetus ought to have under various circumstances and leave it at that. After all, children aren't persons, at least not in the full sense of the word. Their rights are hugely constrained, and we expect little of them as moral agents. We afford them protections commensurate with their situation, and their personhood doesn't really play into it. Personhood for children has implications that are very complicated and that contradict traditional social norms. It is only when we come to those who have attained majority that the concept of personhood has any meaning.
Roe v Wade was, in my opinion, rightly decided. If one accepts that the enumeration of rights in the Constitution is not exclusive and that other rights nonetheless exist, that the notions of what those rights might be can evolve over time, that courts traditionally make law to deal with social developments as they have done in the creation of the evolving common law since time immemorial, and that certain rights carve out areas of life where the government is simply not empowered to act, Roe v Wade rings true. Given the development of jurisprudence vis a vis the 14th amendment and the application of federal constitutional rights to state actions, we can set aside the states' rights objection for the time being. It is one of the few decisions that stand for the proposition that the sovereign's power is not unlimited.