I'll give you a hint - it is never to give women "rights", "autonomy", or "control over their own bodies".
Prior to the political rise of the religious right in the late 1970s, legalizing abortion had pretty mainstream support. Several states with virtually all-male legislatures legalized it, at least in some circumstances, prior to Roe. Conservative and male dominated medical organizations like the AMA wrote briefs in support of Roe. Why?
The reason is that although criminalizing abortion may have been seen as desirable by the male "powers that be" of the time, the cost to them was too high. That cost included the septic abortion wards at every large hospital, and the cost of caring for children in orphanages whose mothers had died from illegal abortion. It also included the cost of caring for the unplanned offspring of women who relied on welfare to raise them.
The cost also included the eroding of respect for government authority that comes from a law being widely flouted by a large cross-section of society, and finally, the profits being made by criminal elements involved in illegal abortions. Pre-Roe abortions weren't always back-alley jobs performed by individual operators. One of my friends from high school had a harrowing experience in 1971 of making arrangements over the phone, then being picked up on a street corner in Chicago by a limo and taken to a motel where a complete operating room was set up, complete with stirrup-table. The cost was $300 in 1971. She's convinced, with reasonable evidence, that it was an organized crime activity.
(edited to avoid tarring the many progressive men who support women's rights) men who are not likely to be swayed by arguments based on women's rights may be induced to support measures that benefit women if they can clearly see the benefit to themselves. Women in Western countries may have come a long way in some respects, but we should still keep this is mind if actual access to abortion and contraception are more important that the ideological point about women's rights. Purely economic arguments that emphasize what's in it for old white men may be more persuasive.