Is there a term for this type of argument?

I’d say as well as the inductive component, there’s an appeal to emotion and/or consequences too.

Somewhere in this thread there is a Hasty Generalisation too - assuming without proof that a particular extreme example can be taken as representative.

The first example is not logically incorrect. Its factually incorrect, if abortion was illegal, and Obama attempted to legalize it, and you know there is a strong possiblity that you mother would have aborted you if it had been illegal, then it it would a logically thing to imply (not quite sure the point you’d be making by this).

Second one could be viewed some form of “ad hominem” attack, that is you are arguing against it by pointing out skulldugery of pro-evolution scientists in the past. Though there is clearly more to it than that.

Also I don’t know if this is the point of using it but, again, the factual content is flawed, while there is some controversy about the conclusions of the peppered moth studies, they were NOT faked (some of the photos were staged but they were purely illustrative and not part of the study.)

Though that may be the case, there’s no reason to believe that it is the case. Working wth the actual information the Op gave we can assume that the speaker knows that their mother would have aborted them if abortion has been as freely as available as Obama wishes it to be. For all we know the person’s mother may have said those exact words.

The OP specifcally said that the speaker was picking the worst example they could find, not theta they were manufacturing untruths. Given that his next example features an exmaple thatis factually correct I don’t think this is meant to be an example of something that contains fatual erros.

As I said in earlier posts, if what the speaker has said is factually correct then there is no logical fallacy here. If what he said isn’t correct then there is still no logical fallacy, there is simply an unwarranted assumption or an outright lie. That may extend as far as becoming a strawman, or it may just be an old fashioned lie.
At this stage petew83 really needs to state quite clearly whether the speaker is telling the truth or not. If they are telling the truth then there is no logical fallacy involved. If they are making unwarranted assumptions then it is perhaps a hasty generalisation, and if they are outright lying then no logical fallacy is required: the statement is factually incorrect. It may also be a strawman, but that is secondary to simply being factually incorrect.

Not in the original example certainly. In that example the speaker says that the consequences of the the policy to himself is representative of unsupportable consequences to himself. There is no implication that it has been extended.

I oppose drink driving because friend of mine was killed by a drunk driver. That isn’t hasty generalistaion. The needless death of my friend alone is sufficient reason for me to oppose DD. Similarly the speaker in the OP finds his own personal death sufficient reason to oppose abortion. That’s not hasty generalisation, it’s a very specific and practical criterion for opposition.

So (If I’m am correct about the OP’s intention) a better example would be this (and I have actually read this kind of thing from Creationists):
“Evolution is wrong because the Piltdown Man was faked”

This, as I said in a previous post, is kind of like a “ad hominem” argument (its detracting from the honesty of pro-evoluion scientists), though has a bit of “strawman” thrown in.

It doesn’t really matter if you can give the poor argument a name or not… as long as you recognize the flaw, point out the flaw directly and move on. It will be much more effective to say “Don’t you see? Your argument fails because of […]; at the step where you’ve […], you went ahead and concluded […], but this inference is unwarranted; after all, it’s always possible that […] and […] instead” than to say “Don’t you see? You’ve committed the Fallacy of the Morchivicated Exponential. Here, look at this webpage! I’ve squeezed a name and a category onto this, though the fit is, admittedly, a bit loose. Still, are you not ashamed at the elements of the decried archetype? Repent!”.

Of course u can never be sure what would have happened, but from his perspective he is telling the truth as best he can assume.
From reading the responses, I have come to belief that my irritation stems from a mixture of bad inductive reasoning (particularly hasty generalization), appeals to emotion, and appeals to consequence (each example might not have all). That’s mainly what i had in mind, thanks.

Um, nuh uh.