So we have a couple of strands to liberalism which I think make good public policy and good personal philosophy.
The key thought – and although most proper philosophers think Mill overrated, he is the go-to guy for my-first-liberalism-workshops – is that you shouldn’t harm other people or restrict their actions unless they’re going to harm you or someone else. Even if they are doing something which you think is a bad idea, like smoking, you should leave them to it. A lot of the debates on abortion really hinge on whether you think a Zygote, Foetus or Embryo is a person who needs protecting or not.
But the harm principle isn’t really the foundation of liberalism, the foundation is the thought “what if I’m wrong?”
That is why we shouldn’t interfere with the actions of others, because my judgement is, in general, only likely to be as good as yours. In specific cases your judgement about your life is, as a rule, going to be better than my judgement about your life.
I don’t have the necessary information to decide things on a case by case basis for you, so it should be left to you. I think that abortion is one of those subjects where even the most voracious critics really have to consider “what if I’m wrong? What is a Zygote/Foetus/Embryo isn’t a person”
Decisions should generally be left to those with the most information and the best incentive to get the decision right. This is a pretty basic, even Hayekian, point. That means, especially with respect to abortion, the woman involved. I don’t think anyone has any more incentive to become au fait with the morality and practice of abortion than a woman considering one.
You might disagree with the decisions of women who choose to have abortions, but they are in a much better position to make that decision than you. Opposing abortion is in much the same ballpark as supporting the smoking ban, the absolute certainty that an outsider knows the best.