Two questions reside here. First, about child abuse rates. Second, about who has abortions. Let me address the second first. The vast majority are for the sake of convenience.
Abortion is used as a means of birth control, to space or limit the number of births.
That brings us to the child abuse rates question. In 1968 Pope Paul VI predicted that, if widespread use of artificial contraception were to become accepted, legalized abortion would follow. So far he has been proven right. The result is pressure to use abortion to make up for the failure of contraception. The reality is that child abuse has skyrocketed because of the cheapening of human life.