Well, I'm pretty bored so I guess I'll just come on here and have a little debate with you. I'll use what you said to start it off, and nothing better to start off a counter-argument with a syllogism (controversial).
P1: A core liberal principle can be considered negative bodily autonomy (inviolable is debatable), individuals may not be forced to provide use of their bodies to others without their voluntary consent.
P2: A right to life (or the moral value of an unborn being) does not logically entail a right to commandeer another person's body; rights to be protected from wrongful killing ≠ rights to positive use of someone else’s biological resources.
P3: Pregnancy necessarily requires prolonged, non-consensual use of the pregnant person's body if continuation is compelled.
C: Therefore, on liberal principles, denying a pregnant person the right to refuse bodily use (i.e., forcing gestation) contradicts the liberal commitment to bodily autonomy; so the claim that of unborn autonomy goes against the pregnant person's bodily rights.
As I've said before, I'm pro-choice so I don't necessarily disagree with your argument (although I would articulate it differently) but I do think the other side has an equally valid argument from the position of liberal rights for which there are only arbitrary counterarguments against, here's what I'd imagine a steelman looks like:
P1: Liberalism upholds the fundamental negative right to life, which prohibits actively killing another human life, especially an innocent one, as a cornerstone of non-aggression and protection of the vulnerable.
P2: The right to life for the fetus entails protection from direct harm or killing, not merely a positive claim on resources; abortion procedures (such as dilation and evacuation) actively kill the fetus through dismemberment or other means, distinguishing it from passively "unplugging" or refusing aid in hypothetical scenarios like organ donation.
P3: Pregnancy often arises from voluntary actions (e.g., consensual sex) that foreseeably create the fetus's dependency, imposing a special parental responsibility to avoid harming one's offspring, unlike cases of forced dependency on a stranger; this responsibility aligns with liberal duties to not abandon or kill dependents one has created.
P4: In exceptional cases like rape, where dependency is imposed without consent, the fetus is still an innocent party not responsible for the crime; ending its life would compound the trauma of the assault with additional violence against an undeserving human, akin to revenge killing which is rightly deemed immoral and illegal in liberal societies, as justice does not permit punishing children for their parents' actions.
C: Therefore, on liberal principles, permitting abortion as a refusal of bodily use overlooks the violation of the fetus's right to life through active killing and parental accountability, contradicting the liberal emphasis on non-violence and responsibility for one's actions; the claim prioritizes one autonomy while ignoring the equal bodily rights of the unborn.
I think this is a sound and logical argument which is just as reasonable and fair as the pro-choice argument on logical and moral grounds. In fact, it might even be a stronger argument because the pro-choice argument you present could be seen as prioritizing some rights over others, or providing a hierarchy of rights, which I'd say is generally illiberal in its approach. Generally speaking, I don't think the strongest arguments for abortion are a woman's "autonomy", though I do think that's valuable.