Making abortion illegal means depriving pregnant women of bodily autonomy. For example, carrying a pregnancy to term is 14 times more likely to end in a woman's death than receiving a legal abortion. Making abortion illegal forces women to assume that risk against their will.
Saying abortion is a matter of conflict of rights (woman's body x soon-to-be new person's body with 50% of DNA not belonging to the woman) is to conveniently forget that adoption is legal. There is no such thing as a conflict of rights when there is at least one option which avoids it.
laws exist to define rights connected to duties, following an isonomy principle. Thus: 1) once abortion is legal, it can't be legal to force a man to take responsability for his child (isonomy) 2) what duties correspond to the right of choosing an abortion? Proving the use of contraception?
There are roughly 700,000 abortions in the US per year, worldwide there are as many as 60million. If there is even a 1% chance that a fetus has human-level moral worth, OR that a fetus has 1% of an adult's moral worth, legal abortion allows 600,000 "morally-as-bad-as-murder" acts per year worldwide.
The best way to prevent abortion is by providing proper natal care, day care, maternal leave and health care for expectant mothers. Making it so that pregnancy isn't a financial and social death sentence is the best prevention for abortion.
The same argument holds true for drugs and guns. Laws dont keep them away.
The cost to society of an unwanted child is much greater than the cost to society of a single abortion. And the people who oppose abortions are usually against the idea of having to pay for anything in society in the first place.