Abortion, competing rights, and the problem with Thomson's violinist argument revisited

(This is a revised version of this post)

No matter what side of the abortion debate a person is on, they often fail to recognize that in the case of abortion there are at least two people involved. Many pro-choicers argue that unborn children should have no personhood status, while many pro-lifers are so focused on the rights of the unborn child that they are unable to make a decent counterargument against "my body, my choice."
I understand why someone would be uncomfortable with anti-abortion legislation. Thomson's violinist argument actually brings up some important points, and then there are similar arguments about bodily autonomy and self-defense.
However, there are things that make abortion unique. Abortion does not simply terminate an unwanted pregnancy; it takes away a life in a very brutal way. The goal of self-defense is to stop the person from attacking you, not to brutally murder them. It is also important to consider the cases in which self-defense happens. Obviously, if there is a possibility that a person could be injured or killed, self-defense would be morally acceptable. Self-defense is also acceptable when the attacker is intentionally trying to take away a person's bodily autonomy, even if the act would not be considered harmful had it been done with the other person's consent. In the case of abortion, the unborn child is innocent. Their intent is not to violate the pregnant person's bodily autonomy, so the unborn child cannot be considered an aggressor. In most cases, the pregnant person's life isn't in danger, either. Therefore, killing would not be acceptable in the case of elective abortion.
Although people can choose not to have children, it is important to consider that, when a parent has custody over a child, they are obligated to take care of them. In most cases, parents can give their children up for adoption if they cannot care for them. In the case of pregnancy, the pregnant person is the only one who can keep the child alive. This isn't about forcing pregnancy or parenthood; it's about the well-being of an already-existing unborn child. If a parent has custody over a child, they have no right to neglect or abandon them. They certainly have no right to abuse them, which is what abortion is. People have the right to abstain from sexual activity or use contraception in order to prevent pregnancy. They do not have the right to harm or neglect an already-existing child. It's fine to not have children, but it is wrong to abuse or neglect a child who has already come into existence.
When I say abortion is a competing rights issue, I am not implying that the unborn child has more rights than the pregnant person. I am saying that, while bodily autonomy is a right, it does not justify aggression.

UPDATE: A variation of this post was featured on Secular Pro-Life's blog. You can read it here.