The sides are, mainly, those of the pregnant woman, the male who impregnated her, the potential person/fetus, and to a lesser extent the extended families of the pregnant woman and the male. One of the most illegitimate participants in the debate are the anti-abortion activists (who disingenuously try to paint themselves as pro-life to imply those opposed to them are anti-life) and who take up the banner of the rights of the fetus but in reality this is just a crock. Their real goal is to force their religion onto others by force of law. The 'rights of the fetus' argument is just a convenient canard for them to use in the attempts to attain their goal.
The rights of the woman to control her own body and the purposes to which it is put are strong and clear. We have abolished slavery and involuntary servitude. There is no justification for forcing a woman against her wishes and at risk to her health and life to carry a pregnancy she does not wish to carry. The facts are that about 1 in 10,000 pregnancies result in the death of the woman. In greater numbers are detrimental health effects from the process. No one should be forced against their will to be subjected to such. Bottom line it is her choice, to be made as she sees fit. She should be reasonable and take input from the male involved in the pregnancy, her family and her doctor (and her clergyperson if that is her style) but none of these should be mandated.
The harder part of the equation is that of the male involved. In cases where both he and the pregnant woman wish an abortion or wish to keep the pregnancy going, there is no problem. But it is where there is a difference of opinion where problems arise. If the man does not wish an abortion and the woman does, he is out of luck. As stated before he cannot, and should not be able to, force the woman to continue the pregnancy to term against her will. But he currently is also nailed if he wishes her to have an abortion and she decides to carry to term. He is liable for up to 21 years of child support payments. In my humble opinion males in such a situation should be able to exercise their choice as well. The woman has the right to decide to have a child. She should not have the right to force someone else to underwrite that choice, especially when they disagree with it. The male should be able to sign a piece of paper giving up any and all claims, rights, etc regarding any produce from the pregnancy. He should pay half the cost of an abortion and give that money to the pregnant woman. At this point he has washed his hands of the entire affair. To do otherwise, as we continue to do now, is to allow men to be enslaved. A woman can seek out men, get them into bed promising they are using birth control, and then when impregnated dump the guy and send him a court order for child support after the birth. Then she can move on to the next guy. There are women who have had 5-10 children of as many men in this manner. They live like queens and never have to work a day in their lives. I find this offensive and my idea would put an end to this practice.
As for the 'rights of the fetus' this is a potential person, not an actual person, and as such has no rights to speak of. Certainly it has no rights which supercede those of the born and existing woman. And also with equal certainty a parasite has no right to an unwilling host. It may seem harsh but this is exactly the situation. There are three types of relationships... self, parasitic and symbiotic. The host woman and the fetus are clearly distinct, therefore self is not applicable. The woman can and could have gone through her entire life without being pregnant or carrying this fetus. It gives her nothing biologically that she requires to survive, and in fact takes from her that which she herself needs for sustenance and pours toxins into her system which her body has to deal with. Clearly this is not a symbiotic relationship, which leaves only a parasitic relationship to describe the situation. And where does a fetus get any rights that no born person has? A person who is born and in need of dialysis cannot just grab someone off the street and hook them up against their wishes. If such a kidnapped person were to detach themselves and leave, even if this action resulted in the death of the other person, they would not be guilty of any crime, much less murder. Why is it that people assume it is any different with a fetus?
Personally I feel that while family and extended family should be allowed input, but that this should not be mandatory, I feel this is where their rights in the decision end.
Now, up to the point of fetal self-viability which happens in the very late 2nd or early 3rd trimester and can be tested for I feel the woman's right to terminate an unwanted pregnancy is absolute. She can do it for any reason she chooses and need have no other person on the planet agree with her for her choice to be valid. At the point of fetal self-viability I feel her choices should be restricted to abort only in the cases of clear and dire threat to her life or health which has been demonstrated as likely in her specific case, or that the fetus is catastrophically defective, such as no brain, half their internal organs, etc, and unlikely to survive after birth without heroic medical measures. Since less than 2% of abortions are performed after fetal self-viability the vast majority of cases do not involve this issue anyway.
All that said, I want to state that I PERSONALLY do not like abortion and have not been party to one in my life. I support other options. But as I said above my broader view is that it is not my place, and I have no right, to force this personal opinion on the matter on anyone else, especially a pregnant woman, by force of law.
Politics