As always, you can find the Dobbs v. Jackson decision here.

The next sentence is a single claim:

“Roe and Casey each struck a particular balance between the interests of a woman who wants an abortion and the interests of what they termed ‘potential life.’ Roe, 410 U.S., at 150 (emphasis deleted); Casey, 505 U.S., at 852.”

Let’s see what the citations show us. Here’s Roe at page 150:

“The third reason is the State’s interest—some phrase it in terms of duty—in protecting prenatal life. Some of the argument for this justification rests on the theory that a new human life is present from the moment of conception. [Footnote 45] The State’s interest and general obligation to protect life then extends, it is argued, to prenatal life. Only when the life of the pregnant mother herself is at stake, balanced against the life she carries within her, should the interest of the embryo or fetus not prevail. Logically, of course, a legitimate state interest in this area need not stand or fall on acceptance of the belief that life begins at conception or at some other point prior to live birth. In assessing the State’s interest, recognition may be given to the less rigid claim that as long as at least potential life is involved, the State may assert interests beyond the protection of the pregnant woman alone.

“Parties challenging state abortion laws have sharply disputed in some courts the contention that a purpose of these laws, when enacted, was to protect prenatal life. [Footnote 46] Pointing to the absence of legislative history to support the contention, they claim that most state laws were designed solely to protect the woman. Because medical advances have lessened this concern, at least with respect to abortion in early pregnancy, they argue that with respect to such abortions the laws can no longer be justified by any state interest. There is some scholarly support for this view of original purpose. [Footnote 47] The few state courts called upon to interpret their laws in the late 19th and early 20th centuries did focus on the State’s interest in protecting the woman’s health, rather than in preserving the embryo and fetus. [Footnote 48] Proponents of this view point out that in many States, including Texas, [Footnote 49] by statute or judicial interpretation, the pregnant woman herself could not be prosecuted for self-abortion or for cooperating in an abortion performed upon her by another. [Footnote 50] They claim that adoption of the “quickening” distinction through received common law and state statutes tacitly recognizes the greater health hazards inherent in late abortion and impliedly repudiates the theory that life begins at conception.

And here’s Casey at page 852:

“These considerations begin our analysis of the woman’s interest in terminating her pregnancy but cannot end it, for this reason: though the abortion decision may originate within the zone of conscience and belief, it is more than a philosophic exercise. Abortion is a unique act. It is an act fraught with consequences for others: for the woman who must live with the implications of her decision; for the persons who perform and assist in the procedure; for the spouse, family, and society which must confront the knowledge that these procedures exist, procedures some deem nothing short of an act of violence against innocent human life; and, depending on one’s beliefs, for the life or potential life that is aborted. Though abortion is conduct, it does not follow that the State is entitled to proscribe it in all instances. That is because the liberty of the woman is at stake in a sense unique to the human condition and so unique to the law. The mother who carries a child to full term is subject to anxieties, to physical constraints, to pain that only she must bear. That these sacrifices have from the beginning of the human race been endured by woman with a pride that ennobles her in the eyes of others and gives to the infant a bond of love cannot alone be grounds for the State to insist she make the sacrifice. Her suffering is too intimate and personal for the State to insist, without more, upon its own vision of the woman’s role, however dominant that vision has been in the course of our history and our culture. The destiny of the woman must be shaped to a large extent on her own conception of her spiritual imperatives and her place in society.

“It should be recognized, moreover, that in some critical respects the abortion decision is of the same character as the decision to use contraception, to which Griswold v. Connecticut, Eisenstadt v. Baird, and Carey v. Population Services International, afford constitutional protection. We have no doubt as to the correctness of those decisions. They support the reasoning in Roe relating to the woman’s liberty because they involve personal decisions concerning not only the meaning of procreation but also human responsibility and respect for it. As with abortion, reasonable people will have differences of opinion about these matters. One view is based on such reverence for the wonder of creation that any pregnancy ought to be welcomed and carried to full term no matter how difficult it will be to provide for the child and ensure its well-being. Another is that the inability to provide for the nurture and care of the infant is a cruelty to the child and an anguish to the parent. These are intimate views with infinite variations, and their deep, personal character underlay our decisions in Griswold, Eisenstadt, and Carey. The same concerns are present when the woman confronts the reality that, perhaps despite her attempts to avoid it, she has become pregnant.

It’s clear through these two passages that the Dobbs claim is accurate. This claim is true:

• “Roe and Casey each struck a particular balance between the interests of a woman who wants an abortion and the interests of what they termed ‘potential life’.”