I assume familiarity with the facts (and if not familiar, they are set out in the opinion.) I will concentrate my arguments on the reasoning to reach a decision. In Roe, Justice Blackmun (whose meandering opinion, especially on medical matters, appears to stem from his experience as counsel for the Mayo Clinic), explained:

The Constitution does not explicitly mention any right of privacy. In a line of decisions, however, going back perhaps as far as Union Pacific R. Co. v. Botsford, 141 U.S. 250, 251 (1891), the Court has recognized that a right of personal privacy, or a guarantee of certain areas or zones of privacy, does exist under the Constitution. In varying contexts, the Court or individual Justices have, indeed, found at least the roots of that right in the First Amendment, Stanley v. Georgia, 394 U.S. 557, 564 (1969); in the Fourth and Fifth Amendments, Terry v. Ohio, 392 U.S. 1, 8-9 (1968), Katz v. United States, 389 U.S. 347, 350 (1967), Boyd v. United States, 116 U.S. 616 (1886), see Olmstead v. United States, 277 U.S. 438, 478 (1928) (Brandeis, J., dissenting); in the penumbras of the Bill of Rights, Griswold v. Connecticut, 381 U.S. at 484-485; in the Ninth Amendment, id. at 486 (Goldberg, J., concurring); or in the concept of liberty guaranteed by the first section of the Fourteenth Amendment, see Meyer v. Nebraska, 262 U.S. 390, 399 (1923). These decisions make it clear that only personal rights that can be deemed "fundamental" or "implicit in the concept of ordered liberty," Palko v. Connecticut, 302 U.S. 319, 325 (1937), are included in this guarantee of personal privacy. They also make it clear that the right has some extension to activities relating to marriage, Loving v. Virginia, 388 U.S. 1, 12 (1967); procreation, Skinner v. Oklahoma, 316 U.S. 535, 541-542 (1942); contraception, Eisenstadt v. Baird, 405 U.S. at 453-454; id. at 460, 463-465 [p153] (WHITE, J., concurring in result); family relationships, Prince v. Massachusetts, 321 U.S. 158, 166 (1944); and childrearing and education, Pierce v. Society of Sisters, 268 U.S. 510, 535 (1925), Meyer v. Nebraska, supra.

This right of privacy, whether it be founded in the Fourteenth Amendment's concept of personal liberty and restrictions upon state action, as we feel it is, or, as the District Court determined, in the Ninth Amendment's reservation of rights to the people, is broad enough to encompass a woman's decision whether or not to terminate her pregnancy. [Emphasis supplied.]

If we read nothing more of the Roe decision, I wonder that anyone would find this reasoning remarkable in the least. Who can deny that, once you accept a right to privacy, that this right extends to a women's control of her body during pregnancy?

Absent denying the existence of a right to privacy, it seems to me inarguable that women's right to privacy must necessarily extend to control of her body, especially during pregnancy.

Interestingly, some, and not just the late Robert Bork, would deny the existence of a constitutionally guaranteed right to privacy. See, for example, Jeffrey Rosen:

Jeffrey Rosen dissents from both Roe and Doe. Like Sunstein, Rosen also focuses on the Court’s proper institutional role, but he argues that the question of abortion rights should be left to legislatures. He takes up many of the arguments made against Roe by John Hart Ely in a famous law review article in 1973. In Rosen’s view, the Court should have stayed out of controversial questions like abortion, because the right to privacy has no basis in the constitution’s text, structure, and history, and the Court’s previous precedents do not require extension of the right to privacy to abortion. Instead of holding that abortion was constitutionally protected, the Court should have allowed the political process to work out the issue of abortion rights. [Emphasis supplied]

I do not find Rosen's argument persuasive, but I think it is a necessary argument for critics of Roe. Rosen, to his credit, understands this.

Other critiques focus on the Roe court's failure to consider an equal protection argument. Riva Seigel argued:

the proper basis of the abortion right is women’s equality, and that the Court’s heightened scrutiny for laws imposing sex discrimination should have begun with Roe v. Wade. Abortion is a constitutional right necessary to secure women’s equal citizenship. Siegel argues that exemptions in abortion statutes like those in Roe and Doe demonstrate, often in quite telling ways, that abortion restrictions are deeply tied to stereotypical views about the sexes and about the duties of women: “Whatever respect for unborn life abortion laws express,” Siegel notes, “state criminal laws have never valued unborn life in the way they value born life.” Instead, states “have used the criminal law to coerce and intimidate women into performing the work of motherhood.” “Abortion laws do not treat women as murderers, but as mothers: citizens who exist for the purpose of rearing children; citizens who are expected to perform the work of parenting as dependents and nonparticipants in the citizenship activities in which men are engaged.” Siegel bases her opinion on the equality arguments offered in amicus briefs submitted to the Supreme Court by various women’s groups. These briefs grounded the abortion right in what we would today call an antisubordination model of equality law. Siegel’s answer to what Roe should have said is to give voice to the lawyers who were part of the legal vanguard of the second wave of American feminism, and whose arguments were largely ignored by the courts.

This is an interesting argument, but, to my way of thinking, not a fair criticism of the Roe opinion. Seigel asks the Court to reach beyond the contours of the equal protection jurisprudence of 1973 (perhaps even of today) and recognize an formulation of equal rights for women that was not recognized in 1973 and maybe, not even today. These are aspirational arguments, but in my view, not a fair basis for criticism of Roe.

Many, like Mark Tushnet, prefer Justice Douglas' formulation of the issue:

Third is the freedom to care for one's health and person, freedom from bodily restraint or compulsion, freedom to walk, stroll, or loaf. These rights, though fundamental, are likewise subject to regulation on a showing of "compelling state interest." [cases omitted]

The Georgia statute is at war with the clear message of these cases -- that a woman is free to make the basic decision whether to bear an unwanted child. Elaborate argument is hardly necessary to demonstrate that childbirth may deprive a woman of her preferred lifestyle and force upon her a radically different and undesired future. For example, rejected applicants under the Georgia statute are required to endure the discomforts of pregnancy; to incur the pain, higher mortality rate, and after-effects of childbirth; to abandon educational plans; to sustain loss of income; to forgo the satisfactions of careers; to tax further mental and physical health in providing child care; and, in some cases, to bear the lifelong stigma of unwed motherhood, a badge which may haunt, if not deter, later legitimate family relationships.

I like this argument as far as it goes, but, I disagree with the idea that there must be a showing of hardship to recognize the right. This does smack of what later becomes the "undue burden" test adopted in Planned Parenthood v. Casey.

Indeed, it is this mindset that informs the question presented regarding when the state can impinge on the right to privacy. Justice Douglas wrote:

Such reasoning is, however, only the beginning of the problem. The State has interests to protect. Vaccinations to prevent epidemics are one example, as Jacobson, supra, holds. The Court held that compulsory sterilization of imbeciles afflicted with hereditary forms of insanity or imbecility is another. Buck v. Bell, 274 U.S. 200. Abortion affects another. While childbirth endangers the lives of some women, voluntary abortion at any time and place regardless of medical standards would impinge on a rightful concern of society. The woman's health is part of that concern; as is the life of the fetus after quickening. These concerns justify the State in treating the procedure as a medical one. [Emphasis supplied.]

Let's repeat that - "voluntary abortion at any time and place regardless of medical standards would impinge on a rightful concern of society." What rightful concern is that one might ask? Justice Douglas does not bother.

Justice Blackmun's Roe opinion is much the superior on this critical point:

On the basis of elements such as these, appellant and some amici argue that the woman's right is absolute and that she is entitled to terminate her pregnancy at whatever time, in whatever way, and for whatever reason she alone chooses. With this we do not agree. Appellant's arguments that Texas either has no valid interest at all in regulating the abortion decision, or no interest strong enough to support any limitation upon the woman's sole determination, are unpersuasive. [...] As noted above, a State may properly assert important interests in safeguarding health, in maintaining medical standards, and in protecting potential life. At some point in pregnancy, these respective interests become sufficiently compelling to sustain regulation of the factors that govern the abortion decision. The privacy right involved, therefore, cannot be said to be absolute. [...] We, therefore, conclude that the right of personal privacy includes the abortion decision, but that this right is not unqualified, and must be considered against important state interests in regulation. [Emphasis supplied.]

It is from this reasoning that the much maligned "trimester structure" of Roe springs:

The pregnant woman cannot be isolated in her privacy. She carries an embryo and, later, a fetus, if one accepts the medical definitions of the developing young in the human uterus. See Dorland's Illustrated Medical Dictionary 478-479, 547 (24th ed.1965). [...] As we have intimated above, it is reasonable and appropriate for a State to decide that, at some point in time another interest, that of health of the mother or that of potential human life, becomes significantly involved. The woman's privacy is no longer sole and any right of privacy she possesses must be measured accordingly.

[...] Physician[s] and their scientific colleagues have regarded that event [quickening] with less interest and have tended to focus either upon conception, upon live birth, or upon the interim point at which the fetus becomes "viable," that is, potentially able to live outside the mother's womb, albeit with artificial aid. Viability is usually placed at about seven months (28 weeks) but may occur earlier, even at 24 weeks. [Emphasis supplied.]

Thus the trimester structure:

(a) For the stage prior to approximately the end of the first trimester, the abortion decision and its effectuation must be left to the medical judgment of the pregnant woman's attending physician. (b) For the stage subsequent to approximately the end of the first trimester, the State, in promoting its interest in the health of the mother, may, if it chooses, regulate the abortion procedure in ways that are reasonably related to maternal health. (c) For the stage subsequent to viability, the State in promoting its interest in the potentiality of human life may, if it chooses, regulate, and even proscribe, abortion except where it is necessary, in appropriate medical judgment, for the preservation of the life or health of the mother.

It doesn't sing does it? But it is reasonable and rational and frankly, the most compelling structure on offer.

We all admire elegant writing. We all bemoan the fact that judicial opinions are not often written in styles we admire. Certainly there is nothing graceful about Justice Blackmun's Roe opinion.

But I have yet to see a compelling argument that the reasoning is not sound. Moreover, I have yet to see an offer of reasoning that is better than Roe could have been in 1973. Remember what Supreme Court judicial reasoning really amounts to, as Justice Brennan famously said - counting to 5.