Because the situations surrounding an abortion can vary, it is a good idea to make sure there's a waiting period. Sometimes women are being bullied into a choice they don't want to make themselves by an abusive relative or boyfriend. Additionally, this ensures they have time to consider all of their options.
Generally, abortions are permitted up to a certain date, (in a way, a type of waiting period). If mandatory waiting periods were applied to abortions that would affect the time permitted to have an abortion. A mandatory waiting period would seem to create more issues regarding abortion. Mandatory waiting periods do not need to be implemented for abortions for that reason.
Abortions are legal in this country, so any measures that discriminate against certain women trying to exercise their rights should not be allowed. Mandatory waiting periods are unfair. Some people cannot take time off work, because they cannot afford it. Others may have to travel long distances to get to a clinic. Making them wait would cost them time and money, that they might not have.
Aside from when the life of the mother is endangered by the baby, abortions should be against the law. It is murder. It was once used only as a method of saving a mother's life, but now it is used as a form of contraception. If I don't want to deal with my dad, should I be able to go through a "mandatory waiting period" and kill him?