The two key issues to focus on are: the nature of a fetus, and the nature of individual rights.
The first issue to grasp is the difference between potential and actual. A fetus is not an actual human being, but is human tissue. A fetus is only a potential human being, just like an acorn is a potential oak tree. That a fetus is potential human being, does not make it an actual one. Once you grasp this point, you need to grasp a much more complex point — which is not self-evident — about the nature of rights.
The second issue to grasp is that rights only apply to actual human beings. Rights only apply to human beings; they apply to human beings because man survives by reason. Men do not survive — at least for long — like animals do in the jungle. Rather then hunting for food like an animal, man grows it. He builds houses to protect himself from hurricanes and storms. He creates clothing to keep warm. He discovers drugs to kill bacteria that may cause him harm. He manufactures refrigerators to keep his food fresh. This is why man has rights — and animals do not — to leave his mind free to think, and his body free to act on that thinking. As a fetus does not use reason to survive; but, rather it survives on the sustenance provided by the body of its’ host, a fetus has no rights, and no need for rights. A fetus has no right to life, liberty, property.
The key issue in this context is that a fetus has no right to be inside the body of another human being, because no such right exists. Yet, this is the only kind of ‘right’ it requires to exist. To grant the fetus such a right, would make its host — the pregnant mother — a slave. Slavery is not a right.
This in essence is the case for a woman’s moral right to abortion: a fetus is not an actual human being, but is only human tissue inside the body of an actual human being. Rights only apply to actual human beings (whether a new born child, or a hundred year old grandfather, or a pregnant woman), as they require freedom to act by the use of their mind.