You can, however, claim that a fetus is not a person and then argue that the fetus is being illegally detained according to the opposing side's logic.

That doesn't seem any different to claiming that if a fetus is not a person according to the opposing sides logic, then there is no point in listening to their further arguments about detainment.

Really, it's ridiculous logic from both sides, I don't see where one side has an argument that is not conflicted by that sides previous assertions.

Presumably because this is in Florida, where the prevailing viewpoint is that a fetus is well past the point where it is to be regarded as a person.