I also wanted to add to some issues WA raised.
Not every pro-choice argument is based on utilitarianism or the future prospects of the child. The primary arguments are a woman's sovereignty over her own body and the fundamental difference between a fetus and a human.
I happen to be in the group that has utilitarian views as well. And the hole in our utilitarian theory is that hypothetically if we have irrefutable proof that the fetus will grow into someone who will cure Cancer and AIDS, then the mother has to bear the child even if she wishes to abort. Such a scenario would not be pro-choice.
At the same time a pro-life person cannot claim that their stance is based on "fair chance". The primary argument is based on the sanctity of human life and that there is no philosophical difference between a fetus and human life. A fair chance theory will need to be tossed out if there is statistical data for the contrary.
Also to put the gross generalizations in context. I cannot speak for all across the world, but this is very true in the American political landscape. A lot of the conservatives who oppose abortion and euthanasia also oppose welfare, education grants, low income project housing, subsidized health care and many such social services. They deem it as entitlement. They believe that people who cannot afford to take care of themselves or their family are stupid, lazy and society should not support them. The opposition to social infrastructure is contradictory to a pro-life claim. It prohibits abortion and euthanasia, but at the same time refuses to give people the means to sustain a healthy productive lifestyle.
On the other hand liberals who support abortion and euthanasia do support social infrastructure. Supporters of abortion don't promote it or encourage it. No one wants to hand abortions out like candy. No one is telling poor people, single mothers etc that they should not have children. It should be a carefully considered decision after weighing all the options. Should people lacking resources choose to have a child it is not the child's fault. Society needs to chip in so that the child can get food, medical care, education and opportunities. Should a child be born with medical problems or get one down the road, it should not be a lottery whether the family can afford it or not, people should not have to go broke or neglect other responsibilities to fulfill a moral obligation. Society needs to chip in if everyone who deserves and wants to live, gets that chance to live.
The other thing I don't get is the conservative argument against condoms, birth control and morning after pills. If you are so opposed to abortion, wouldn't you want to prevent unwanted pregnancy at least?