Inversion involves using the opponent’s argument against them by reversing the direction of their reasoning. That is, their argument is turned on its head. If we reach a dubious or absurd conclusion (see reductio ad absurdum) then we have reason to assume the original argument is suspect.
For example, Shamoo Shabang is opposed to embryonic stem cell research. She says: You can't destroy an embryo as each is a "potential life".
Her friend Olive Olivers responds by pointing out: The basics of biology tell us that there are many stages in the development of life. Given this, it seems rather arbitrary to say the "potential" begins with fertilisation.
She goes on to invert Shamoo's argument by heading in the other direction: Before fertilisation we have the "potential life" of each sperm and ovum (each of them, potentially, could fuse and start off the whole process). If we follow the "potential life" reasoning we ought to attribute them this moral status too. This is patently absurd.
She has given a reason to assume the "potential life" argument is suspect.
Of course, Shamoo understands inversion also, and inverts Olive's inversion: If I granted that argument any validity, then surely we can go the other way? Concluding that there is no point at which we can attribute "potential life" to a gestating human, and as a consequence award no moral status to any unborn child? Clearly, you'd agree, that's an abhorrent position.
In using embryonic stem cells as an example, it is worth noting that people who hold the "potential life" view follow a deontological ethic, as opposed to a consequentialist ethic (which tends to be argued by those in favour of research using embryonic stem cells). There are advantages and disadvantages, as there are philosophical and practical problems, with both ethical systems. Since the dawn of moral philosophy, both types of ethics, as argued by all their various proponents, either lack credibility (due to some of their conclusions), or are not self-consistent (have internal contradictory aspects). Given people are arguing about embryonic stem cell research from incompatible a priori positions, a conclusion satisfactory to both sides may never be reached.
Examples of Inversion: