Here is a simple version of the Potentiality Argument (PA):
1. All potential persons have a right to life.
2. The human fetus is a potential person.
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3. The human fetus has a right to life.
Does PA 'prove too much'? It does if the proponent of PA has no principled way of preventing PA from transmogrifying into something like:
1. All potential persons have a right to life.
4. Everything is a potential person.
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5. Everything has a right to life.
One kind of probative overkill objection is easily sent packing, namely, the sort of objection that is based on the confusion of potentiality with the mere logical possibility of transformation. It is thinkable without contradiction that a pumpkin seed become a rabbit. Indeed it is thinkable without contradiction, and thus logically possible, that anything become anything. But of course a potentiality is something quite specific and has nothing to do with an empty logical possibility of transformation. After all, we know that pumpkin seeds do not become rabbits; they become pumpkins. Rabbits give birth to rabbits, not kangaroos or pumpkins. Nature is orderly. If there are potentialities in nature, they are directed at specific outcomes. They are like dispositions in this regard. Solubility is the disposition to dissolve, not the disposition to shatter or explode. And just as a disposition can go unmanifested, a potentiality can go unrealized. But to say that a potentiality can go unrealized is not to say that the potentiality is not itself something real, indeed something actual. Anyone with an elementary grip on the notion of potentiality can see that the first kind of overkill objection fails.
According to a less crude objection, there is no principled way to ascribe potential personhood to a zygote without also ascribing it to spermatazoa, unfertilized ova, and pairs of sperm cells and egg cells.
Let's consider first the pair (S, O). Let S be one of my sperm cells and O an unfertilized egg cell of a nun in India. This pair exists because its members exist. But this pair is not a potential person. The very idea is incoherent. For one thing, a pair is either a set or a set-theoretical construct, and as such an abstract object; but surely no abstract object has the potentiality to become a concrete individual person. But whether or not pairs are abstract objects, the notion that the pair in question is a potential person is absurd on the face of it. For a sperm cell out of all contact with an egg cell simply cannot develop into a person. "It takes two to tango."
Now consider a sperm cell S. Given that there are potentialities in nature, S has the potentiality to fertilize an egg. But as noted, potentialities are directed to specific outcomes. The potentiality to fertilize an egg is not the potentiality to become a person. Surely, a sperm cell out of all relation to an ovum does not have the potentiality to become a person.
But in rebuttal someone might argue as follows:
a. Had S penetrated O, then zygote Z would have resulted.
b. Had Z resulted, then Z would have become person P.
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c. Had S penetrated O, then Z would have become P.
The idea behind the rebuttal is that S's power to penetrate and thus fertilize O can be represented by the subjunctive conditional (a), and zygote Z's potential to become a person can be represented by subjunctive conditional (b). But then it seems to follow that S's potentiality to fertilize O is a potentiality for S to become a person.
The trouble with this rebuttal is that it assumes transitivity. Transitivity fails, however, for subjunctive conditionals. Consider:
d. If J Edgar Hoover had been born a Russian, then he would have been a communist.
e. If J Edgar Hoover had been a communist, then he would have been a traitor.
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f. If J Edgar Hoover had been born a Russian, then he would have been a traitor.
This is clearly an invalid argument; its invalidity is due to a failure of transitivity in the case of subjunctive conditionals. The (a)-(c) argument is similarly flawed. So the rebuttal fails.
As for an unfertilized egg O, we can say that it has the passive potentiality to be penetrated and fertilized. But this is not to say that it has the active potentiality to become a person.