There are many sound secular arguments against abortion, but the above is not one of them.
There are many types of medical procedures which often (or in some cases inevitably) cause considerable stress or harm to the patient, but may sometimes be better than any available alternative. I think even the most ardent supporters of abortion would say (at least publicly) that it is better for a woman to avoid getting pregnant than for her to get pregnant and have an abortion, if for no other reason than the fact that getting pregnant and having an abortion is bound to be more stressful and less safe than simply not getting pregnant in the first place.
Of course, the more fundamental issue is that people who are deathly afraid of getting pregnant are far more likely to refrain from behaviors that would cause pregnancy than those who have no such fear. Liberals claim that "kids are just going to 'do it' anyway", but somehow in the a lot of kids managed not to. There's no reason kids shouldn't be able to manage that today.