The following is an abortion argument one often hears. It is sometimes called the Woman's Body Argument. I will argue that it is not rationally compelling.
1. The fetus is a part of a woman's body.
2. A woman has the right to do whatever she wants with any part of her body.
Therefore
3. A woman has the right to do whatever she wants with the fetus, including having it killed.
For this argument to be valid, 'part' must be used in the very same sense in both premises. Otherwise, the argument will fall afoul of the dreaded quaternio terminorum, the four-term fallacy. There are two possibilities. 'Part' can be taken in a wide sense that includes the fetus, or in a narrow sense that excludes it.
If 'part' is taken in a wide sense, then (1) is unexceptionably true. Surely there is a wide sense of 'part' according to which the fetus is part of its mother's body. But then (2) is reasonably rejected. Abortion is not relevantly like liposuction. Granted, a woman has a right to remove unwanted fat from her body via liposuction. Such fat is uncontroversially part of her body. But the fetus growing within her is not a part in the same sense: it is a separate individual life. The argument, then, is not compelling. Premise (2) is more reasonably rejected than accepted. Indeed, one can say that the argument begs the question at (2). For one cannot know (2) to be true without knowing (3) to be true.
If, on the other hand, 'part' is taken in a narrow sense that excludes the fetus, then perhaps (2) is acceptable, but (1) is surely false: the fetus is plainly not a part of the woman's body in the narrow sense of 'part.' I wrote "perhaps (2) is acceptable" because it is arguable that (2) is not acceptable. For a woman's body is an improper part of her body; hence if a woman has a right to do anything she wishes with her body, then she has a right to kill her body by blowing it up, say. One who has good reason to reject suicide, however, has good reason to reject (2) even when 'part' is construed narrowly. And even if we substitute 'proper part' for 'part' in the original argument, it is still not the case that a woman has a right to do whatever she wishes with any proper narrow part of her body. Arguably, she has no right to cut out her own heart, since that would lead to her death.
My conclusion, then, is that the Woman's Body Argument is not rationally compelling. Indeed one can easily 'run it in reverse' with no breach of logic:
1. The fetus is a (wide) part of a woman's body.
~3. A woman has no right to do whatever she wants with the fetus.
Therefore
~2. Some (wide) parts of a woman's body are such that she has no right to do whatever she wants with them.
The 'forward' argument and the 'reverse' argument cancel each other. This shows that neither one, taken by itself, is rationally compelling.