And nobody is stopping any woman from taking an abortifacient and inducing her own abortion. Women still do this around the world every day, even in countries where abortion is legal and offered by the state.
However, self-induced abortion is generally very painful and bloody and nasty, is not guaranteed to be effective, and carries a significant risk of serious injury or death for the mother. In a civilised society, we recognise that many women are desperate enough to go through with it, anyway, so the medical profession provides this service in order to take away much unnecessary suffering and trauma, and to make the process as pain-free, risk-free and effective as possible.
You could say (and you'd be right) that state-assisted abortion results in abortions and loss of life that otherwise wouldn't go ahead - that it "encourages" abortion - in the same way that the anti-euthanasia contingent argue that state-assisted suicide "encourages" suicide.
The parallels are very strong and are not raised enough.
Only abortion is arguably "worse" from this POV, because it involves a consenting adult asking the state to end another (albeit dependent) life, rather than a consenting adult asking the state to end their own life.
Surely one ought to have more power over one's own life and death than that of another being? Therefore, I don't see how anyone pro-abortion can be anti voluntary euthanasia.