Dissent

"Even if there were a plaintiff in this case capable of litigating the issue which the Court decides, I would reach a conclusion opposite to that reached by the Court. I have difficulty in concluding, as the Court does, that the right of "privacy" is involved in this case. Texas, by the statute here challenged, bars the performance of a medical abortion by a licensed physician on a plaintiff such as Roe. A transaction resulting in an operation such as this is not "private" in the ordinary usage of that word. Nor is the "privacy" that the Court finds here even a distant relative of the freedom from searches and seizures protected by the Fourth Amendment to the Constitution, which the Court has referred to as embodying a right to privacy. Katz v. United States, 389 U.S. 347 (1967)."

http://womenshistory.about.com/library/etext/gov/bl_roe_j.htm

"If the Court means by the term "privacy" no more than that the claim of a person to be free from unwanted state regulation of consensual transactions may be a form of "liberty" protected by the Fourteenth Amendment, there is no doubt that similar claims have been upheld in our earlier decisions on the basis of that liberty. I agree with the statement of MR. JUSTICE STEWART in his concurring opinion that the "liberty," against deprivation of which without due process the Fourteenth [410 U.S. 113, 173] Amendment protects, embraces more than the rights found in the Bill of Rights. But that liberty is not guaranteed absolutely against deprivation, only against deprivation without due process of law. The test traditionally applied in the area of social and economic legislation is whether or not a law such as that challenged has a rational relation to a valid state objective. Williamson v. Lee Optical Co., 348 U.S. 483, 491 (1955). The Due Process Clause of the Fourteenth Amendment undoubtedly does place a limit, albeit a broad one, on legislative power to enact laws such as this. If the Texas statute were to prohibit an abortion even where the mother's life is in jeopardy, I have little doubt that such a statute would lack a rational relation to a valid state objective under the test stated in Williamson, supra. But the Court's sweeping invalidation of any restrictions on abortion during the first trimester is impossible to justify under that standard, and the conscious weighing of competing factors that the Court's opinion apparently substitutes for the established test is far more appropriate to a legislative judgment than to a judicial one."

http://womenshistory.about.com/library/etext/gov/bl_roe_j.htm

Basically what Mr. Justice Rehnquist is saying is that the issue is not about privacy. It's about civil liberty. It's about getting a law passed so that there will be the liberty to have an abortion without having any penalty in doing so.