Sure we do. All the bloody time.
First, you've changed the subject: arguing that laws should reflect the majority opinion is different from saying that there's no dispute, you're merely arguing for a particular method of dealing with the dispute. Second, have you forgotten already that the Supreme Court's Roe v. Wade ruling removed much of the issue from democratic consideration? Third, what is legal is different than what is moral, and what the law is can diverge from what the law should be. There's nothing illogical about having a belief which contradicts the law or majority opinion, nor is there anything wrong with wanting to change the law and convince your fellow citizens to help do that.
That is a tactical decision which tells us nothing about the rightness or wrongness of either position. Furthermore, it's not even obvious that this is the right tactical decision (see: slavery and the Civil War).
Except again, you're assuming things which are in dispute. You are appealing to the interests of the pregnant woman who wants an abortion (the person whose actions are being controlled), but ignoring the interests of the fetus, because you do not think the fetus has interests worthy of equivalent consideration. But not everyone agrees on this point. If the fetus has similarly important interests, then preventing the death of that fetus is less onerous than preventing an abortion, because death is basically the biggest restriction possible on someone's freedom.