Consequently, even if it is better for p to exist than not to exist, assuming she has a life worth living, it doesn’t follow that it would have been worse for p if she did not exist, since one of the relata, p, would then have been absent. What does follow is only that non-existence is worse for her than existence (since ‘worse’ is just the converse of ‘better’), but not that it would have been worse if she didn’t exist.
The footnote that expands on this:
Rabinowicz suggested this argument already back in 2000 in personal conversation with Arrhenius, Broome, Bykvist, and Erik Carlson at a workshop in Leipzig; and he has briefly presented it in Rabinowicz (2003), fn. 29, and in more detail in Rabinowicz (2009a), fn. 2. For a similar argument, see Arrhenius (1999), p. 158, who suggests that an affirmative answer to the existential question “only involves a claim that if a person exists, then she can compare the value of her life to her non-existence. A person that will never exist cannot, of course, compare “her” non-existence with her existence. Consequently, one can claim that it is better … for a person to exist … than … not to exist without implying any absurdities.” Cf. also Holtug (2001), p. 374f. In fact, even though he accepted the negative answer to the existential question (and instead went for the view that it can be good but not better for a person to exist than not to exist), Parfit (1984) came very close to making the same point as we are making when he observed that there is nothing problematic in the claim that one can benefit a person by causing her to exist: “In judging that some person’s life is worth living, or better than nothing, we need not be implying that it would have been worse for this person if he had never existed. --- Since this person does exist, we can refer to this person when describing the alternative [i.e. the world in which she wouldn’t have existed]. We know who it is who, in this possible alternative, would never have existed” (pp. 487-8, emphasis in original; cf. fn. 9 above). See also Holtug (2001), Bykvist (2007) and Johansson (2010).
I think my argument builds off the following from “The value of existence” by Gustaf Arrhenius and Wlodek Rabinowicz (2016):
The footnote that expands on this: