Your analogy doesn't work. An egg is more like a placenta...

Umm, no. An egg shell might be like a placenta, or maybe even an egg white but the egg will hatch into a bird a placenta won't. What do you think the yolk is? The analogy holds. At what time is an egg a bird? When it forms the shape of a bird inside the egg? When it hatches? It is an arbitrary point we designate.

As far as 'viable,' that is an arbitrary measure. A baby is viable for so long. A homeless person is viable for so long. Realistically, we are only as viable as our health.

This is a bit of an equivocation on the word viable. Surely you can see the difference between a fully grown adult homeless person and a still developing fetus. It is not so arbitrary when you look at it in context and 25 weeks is roughly when a fetus can continue to live with help outside of the womb, any sooner and the chances plummet to an extreme.

The question of "person-hood" is arbitrary.

Agreed. The line being drawn at viability or brain activity is just where ethics say the most humane approach would be if abortions were to occur.

Usually the decision is being made by immature, irresponsible, selfish, horny, young adults without the means to raise a child and whose future would be hampered by a child.

I would ask for a citation for such a generalization of "usually". I know this is what people like to think who is getting abortions but really it is just conjecture. I think the makeup is a little more complicated than that. Possibly in your case could this be projection due to your personal history? Of course this representation does make up a portion of the abortions but I don't think it is the majority. I would think the majority have more to do with poverty than horny teens. We may disagree to some degree of attribution here but it is no secret that the poor have more abortions than the wealthy.

"I could be swayed I would think if the pro-choice side would not use such hyperbolic tactics as 'a fetus is a parasite,' hiding behind 'woman's rights to her body,' appeals to emotions for women who are victims of rape or incest, etc."

While I disagree with many pro life arguments for similar reasons I think some of those examples are a bit off. Appeals to emotion considering rape or incest are also called "legal fictions" having real incidents that have come to light. To dismiss these as a fallacious appeal to emotion is to ignore the reality that people live. It is slightly off my point I failed to make too;

What type of things people value and what the arguments they are using to convey an idea do not often reach across the isle. Conservatives generally value in group cohesiveness more than their liberal counterparts do. Liberals generally value fairness more than their conservative counterparts. Many debates about abortion use tactics that are really preaching to the choir rather than trying to sway those that oppose them. For instance;

Belittling others for their beliefs is a pull towards group cohesiveness. Someone who values the group more than another may find these actions to change their stance. As for the legal fiction above, those are appeals to fairness and those arguments will likely fall flat on someone across the isle.

To reach across the isle one would have to craft an argument that resonates with their opponents values, not their own. In abortion debate we rarely see this. We instead see the sides digging in to their respective opinions. This is why I note that "I could be swayed I would think if..." bit.

Overall we have similar views on this subject but differ on a few "cogs".