You need to take this one back to the drawing board, or choose a topic that you have the necessary understanding of to make an informed argument.
"Women should be able to have an abortion if they are too young and unable to take care their babies."
So, in short, you admit that this is a matter of convenience. She is not "unable", to take care of her baby. Sure, it may make her life harder to take care of it, and she might have to endure a lot of sacrifice, but in most countries, especially developed countries which I assume the audience you are speaking to resides in, I have never heard of babies dying due to lack of sufficient means. The mother can receive government assistance to help her support the baby, and if all else fails, she can always give the baby up for adoption. This rationale in quotes, is a product of a selfish mentality, which is probably the reason for the dilemma in the first place. She may be too young to care, but someone else isn't. And in another unlikely scenario, she may find that she is unable to care for the baby, but someone else isn't. So, if it is going to disrupt your life so much that you'd rather not take care of the baby, have someone else do it for you. And you can't have it both ways; you can't decide that, oh but I don't want someone else to have my baby, especially at the expense of killing a life altogether. The notion that a mother's self-inflicted dilemma -- not that of killing the fetus or not, which is no dilemma, but the decision on whether she should derail her own fastidious plans, (which probably won't go as planned after all, if history is any judge) for her baby's sake, or give the baby up for adoption, is not an easy one, is true, however, it is entirely of her own doing. Your point is formally deconstructed when we look at the real options, in real terms.
Do we kill your aspirations or desires, or do we kill a life?
"And the right to have an abortion if the pregnency negatively affects the women's or the babies's health."
This point is far, far above the one preceding it, in terms of credibility. If there are very serious risks to the woman's health, an abortion could be justified on the grounds that you choose the lesser of two evils, that is, forsaking the unborn child to save the mother's life. The baby's health is another question altogether. It's no doubt hard to make a decision for someone on whether or not their life is worth living, but I could see how a severe deformity might lead one to the route of abortion, justifiably.
"Having control over their own bodies is an important part of the equal rights that women have fount for."
Look, by all means, having control over "their own bodies" does not extend to the life of the fetus. If we implant an embryo in a surrogate mother, then doesn't she have the right to abort the child, without regard for any preconceived agreements, because she has liberty over "her own body?
"Her own Body" is understood to mean a permanent part of her inherent physical anatomy, separate from an independent life which she has no right to have reign over.
"Another reason that women should be able to have abortions is in case the mothers are too young and unable to take care their babies. Unwanted pregnancies can be very stressful for women. Therefore, if they think they can not give their babies a good life then it is right for them to have abortions."
This is mostly a repetition of the first point, in poor arrangement, due to poor sentence progression mechanics. But you interjected some new things. First you say that "an unwanted pregnancy can be very stressful."
Guess what? Driving in heavy traffic can be very stressful, but that doesn't give you the right to kill every driver and passenger of every car on the highway, or any for that matter.
Shortly after that, I was forced to wince as I read your subjective evaluation of what is a "good life."
Consider this, it's some real Sh**: There are people living in Southeast DC, not more than 15 miles from where I live, who subsist on scraps, and sleep in degenerate buildings with basketball-sized rats, where the sound of gunshots is not at all foreign. Outside, they face the bereft reality that is rampant drug dealing, unconcealed crime and violence, and conditions that to anyone unaccustomed, would be untenable. Yet still, they value their life.
Rene-Thierry Magon de la Villehuchet, he was a french fund manager, one of thousands of victims of the now infamous Madoff Scandal. Why do I say he "was?"
He committed suicide after losing $1.4 billion of his clients' money in the Ponzi Sceme.
He could have still maintained a quality of life that some people spend their whole life dreaming of. But in the end, he valued money more than his life. What life he had was not "good" enough for him.
I make that comparison to show you the extreme difference of opinion on what makes a life worth living, that really, there is no way to determine for somone else, what is a "good life."
"Therefore, it is right if a woman chooses to get abortion in this case."
I've already mentioned how it's largely ridiculous to assume decisions for other people, especially on the most important question of their life; that is, of, their life, I should say.
But suppose even that there is a gray area that "might" justify a woman getting an abortion. The abortion would not be "right." That would mean that doing nothing is wrong. So leave it open for interpretation with a word like "might" "perhaps" "possibly" "could" etc.
What I'm saying is that if the situation might have justified it 99.9% to get an abortion, you cannot go beyond that premise to 100%, and say that it is "right", without first clearly defining the motivating factor in terms of % justification of the abortion. Not only is that impossible to do objectively, it would be hard to do subjectively based on the variability of different health concerns, or risks. Therefore, take my advice and use a moderate word such as "might", "perhaps", etc.
"One advocate of abortion is Stone. For Stone, " death seriously harms the fetus and so the fetus has a right to life"
Advocate means someone in support of. You've misused the word throughout your essay. Take that into consideration when you write your new essay.
It seems that you manage to repeat the weakest, poorly articulated points in your argument a few more times.
In your conclusion, it seems you finally decide to throw the word "rape" into the mix as an afterthought.
That would probably recur many times in the body, if not as early as the thesis, in a well written persuasive essay on either side of this topic, but even more so in support of abortion.
As someone who does not have an expert grasp on the arguments, you need to stick to the more salient points such as rape, extreme deformities, serious health risks to the woman, etc.
Stick to those extenuating circumstances and you'll have a better chance of writing a good persuasive essay.
I hardly addressed the conventions of good writing, choosing rather to focus on the content, but there is also much room for improvement in the intro, body, and conclusion.
The intro has 2 major aspects. The opening sentence and thesis, both of which need improvement. The body is simply your ability to expand on those points, and organize and coordinate your arguments. Your conclusion will summarize why your thesis is right, and memorably no less. It will not include new ideas.
Practice makes perfect.