Many people who oppose legal abortion or who only weakly support legal abortion will often focus their objections on the idea of "abortion on demand." They see something wrong with abortion being readily available. But if abortion is not available when women want it ("on demand"), what is the point of it being legal? If abortion is legal because women should be able to make autonomous decisions about what happens to their bodies, how can abortion not be made available when they demand it?
The answer is that people who oppose abortion on demand oppose the idea that women can be trusted to make autonomous decisions about what happens to their own bodies, an attitude which can be traced directly back to traditional, patriarchal, religious attitudes towards religion. This is most clearly the case with anti-choice activists who don't hide the fact that they want the state to have the power to make decisions for women, but it's also true for weak abortion supporters. They agree to the imposition of waiting periods, required sonograms, and other measures which imply that they don't really believe that a woman who goes to a clinic for an abortion has thought it through, knows what she is doing, or can be trusted to make the right choice.
In Why I Am An Abortion Doctor, Suzanne T. Poppema writes:
[W]e would eschew self-imposed waiting periods and do the procedures the very same day. Our attitude was: We trust women to have already thought very seriously about the abortion and all their alternatives before they come to us, and we respect the decision they make. [...]
My belief was that of course women are moral agents and would have thought about their options and decisions before coming here. Of course there shouldn’t be a rule that you have to (a) have your physical exam, then (b) have all your options counseling by somebody else, and then (c) have to go home and think about it, and then (d) come back another day. We don’t call this sort of runaround “intimidation” anymore, though that’s precisely what it amounts to. Instead, lawmakers lump all this procedural hoop-jumping together under the label “informed consent,” which is a euphemism for “women can’t possibly know what’s best for their own bodies so we’re going to insist that they sit and listen to what the state thinks they should hear.” [...]
A woman who comes to see us about abortion needn’t explain herself or her situation to us. If she wants to end a pregnancy, that’s her business, not ours — and certainly not the state’s. It never ceases to amaze me to hear the expression: “Abortion on demand.” What would the alternative be? Abortion by prayer? By edict? Upon seeking consensus? After groveling? Women have thought long and hard about this decision before they ever get to my clinic. In fact, most of them have been agonizing for days or even weeks, some to the extent of rescheduling their appointments several times. [emphasis added]
Religious conservatives would like to place all sorts of restrictions on women’s ability to obtain abortions. They can’t ban abortion outright, but they can perhaps make abortion so difficult to manage that women will be less likely to choose it — thus making it a theoretical choice, but not a practical choice. This is already the situation for many women in America because abortion providers are located much too far away to reach conveniently even if they could obtain an abortion on the first visit, never mind if they are required to make a second appointment after a waiting period.
Poppema is right — what she describes above is a form of intimidation. Anti-choice activists don't approve of the choices which some women make and, not being able to ban those choices outright, engage in manipulation, intimidation, and outright bullying in order to make those choices more difficult to realize. That is their ultimate goal — not things like education, as they like to claim — and that's why such intimidation must be prevented.
The intimidation being used by the Christian Right is justified be their conviction that women cannot be allowed or trusted to make these moral decisions themselves — that the state knows better what should happen to a woman's body than she does. The intimidation assumes that unless the state intervenes, women can't be trusted to think this through, to inform themselves, or to understand what they are doing.
Polices like waiting periods may sound reasonable in isolation because who wants to argue that there is something wrong with stopping to think about a serious decision? If this were a reasonable justification for waiting periods with abortion, it would also justify waiting periods before voting — but who would deny that forcing people to go to polling stations twice or more (especially if they are difficult to reach) would be a form of disenfranchisement?
Women's choices about what happens to their own bodies must be respected if women's equality and autonomy is to be respected. It's paternalistic to assume that they haven't already thought about their choices and that they need more time, perhaps in the hope that they will make a different choice altogether. It's true that some women may regret their choice to have an abortion, but part of being an autonomous adult is making choices you may regret later and living with that.