Now: here's the thing about this game. It's easy. It's easy because neither of us is wedded in identity or ego to the outcome. It is merely an exercise in evaluated argument schema. I didn't even take a position on the issue here, I simply responded to invalidity issues in your argument. This is nothing like politics as it really happens. The arguments aren't soldiers. I'm not trying to win. We haven't taken sides. So our minds will be fine. But it won't prove anything.
we've already answered the question in court
We've also already answered the abortion question in court (I assume the context is the American legal system...) if that criteria is sufficient to establish one of your premises it should be sufficient to establish the issue in it's entirety. Conversely, if the abortion question is up for debate, so too is the sheltering newborns from the elements questions.
of whether or not we can be forced to act in a child's best interest against our will
The government can legally force me to pay income taxes against my will. That does not settle the question of whether or not the government can legally force me to do anything against my will. For instance, most people do not believe it is legal for the government to secretly lock me up and torture me without due process. Similarly, there being an obligation to shelter newborn infants does not settle the question of the extent of the sacrifices a government can require of parents for their children. Presumably there are some sacrifices you would find onerous.
I argue that all human lives have moral value,
Your terms are ambiguous and the substance of the issue lies in their definitions. In particular, you appear to beg the question about when in fact human life begins. Those who support a legal right to abortion often deny that human life begins at conception and have various reasons for this view.
In conclusion 1) the argument you use for one of your premises also argues for the inverse of your conclusion, 2) your subconclusion that women can be forced to be incubators if fetuses are humans does not follow from your premise and 3) you provide no argument for the claim that fetuses are human lives
[META] I'm not trying to win for a reason; it would be improper for me, a person who loves to argue about politics, to create a "test" in which I conveniently get to argue about politics with a community which has a prohibition against arguing about politics; I felt that there would be an implicit ethical violation there. I chose that argument specifically so I wouldn't get sucked in. Yeah, the axiom I chose was kind of poor; it's not a position I regularly argue from. Fortunately, even faulty arguments are good for this test. (And holy crap staying uninvolved is going to be hard. I had to erase my counterarguments four times while writing this.) [/META]
Or is the convention against discussing politics here silly?
I propose a test. I'm going to try to lay down some rules on voting on comments for the test here (not that I can force anybody to abide by them):
1.) Top-level comments should introduce arguments (or ridicule me and/or this test); responses should be responses to those arguments.
2.) Upvote and downvote based on whether or not you find an argument convincing in the context in which it was raised. This means if it's a good argument against the argument it is responding to, not whether or not there's a good/obvious counterargument to it; if you have a good counterargument, raise it. If it's a convincing argument, and the counterargument is also convincing, upvote both. If both arguments are unconvincing, downvote both.
3.) Try not to downvote particular comments excessively, if they're legitimate lines of argument. A faulty line of argument provides opportunity for rebuttal, and so for our test has value even then; that is, I want some faulty lines of argument here. If you disagree, please downvote me, instead of the faulty comments, because this post is what you want less of, not those comments. This necessarily implies, for balance, that we not excessively upvote comments. I'd suggest fairly arbitrary limits of 3/-3?
Edit: 4.) A single argument per comment would be ideal; as MixedNuts points out here, it's otherwise hard to distinguish between one good and one bad argument, which makes the upvoting/downvoting difficult to evaluate. (My apologies about missing this, folks.)
I'm going to try really hard not to get personally involved, except to lay down a leading comment posing an argument against abortion, a position I don't hold, for the record. The core of the argument isn't disingenuous, and I hold that this argument is true, it just doesn't lead to my opposing abortion. I do not hold the moral axiom by which I extend the basic argument to argue against abortion, however; I'm playing the devil's advocate to try to help me from getting sucked into the argument while providing an initial point of discussion.
Which leads me to the next point: If you see a hole in an argument, even if it's an argument for a perspective you agree with, poke through it. The goal is to see whether we can have a constructive political argument here.
The fact that this is a test, and known to be a test, means this isn't a blind study. Uh, try to act as if you're not being tested?
After it's gone on a little while, if this post hasn't been hopelessly downvoted and ridiculed (and thus the premise and test discarded as undesirable to begin with), we can put up a poll to see whether people found the political debates helpful, not helpful, and so on.