Don't think that I am shredding you here. This is a very well-written essay, but there are ways that you can make it stronger. Here are a couple of quick thoughts:
"Hills Like White Elephants"
This should be in italics instead of quotation marks. Quotation marks are generally reserved for more minor works.
Ernest Hemingway's "Hills Like White Elephants" depicts the story of a young woman faced with the decision of abortion.
This is getting picky, but I'd like to see "faced" changed to "facing" (and then drop the word "with").
As the story progresses in intensity
Progresses and intensifies? It isn't just progressing in intensity ...
Drop the word "seems." It is too wishy washy for your opening paragraph.
dialogue would be the more common spelling
I feel like there is something missing at the end of your first paragraph. Something like a thesis. If your teacher doesn't expect a thesis, fine. As a reader, I want to know what argument you will be making, what point you will be exploring, what theme you took from the literature.
It is quite obvious that the author sympathizes with the girl simply through making her.
making her? Making her what? Portraying her as vulnerable? This needs to be expanded.
The dialog also reveals the author's attitude towards the girl by showcasing her as a submissive[,]
controlled by the man.
She says, "Then I'll do it. Because I don't care about me," showing that she is in love with this man and seeks his approval and happiness.
This sentence is a little unclear. I think you need to let the reader know that "it" is abortion in your set up. I would also say, "his approval and his happiness" so that the reader is clear that it she isn't merely seeking happiness.
Her submissive nature to the man's wishes over her own shows the author's pity towards the girl who is unable to express her emotions.
"Her submissive nature" speaks to a lot more than just her being submissive to the man. Maybe change that to just, "Her submission to the man's ..."
It is apparent that she wants to keep her child even if it is a white elephant and will only cause her to give everything up .
Put "white elephant" into quotes; we aren't talking about a literal white elephant here. Be clearer on what "everything" is that she will be giving up. Expand the thought here.
Hemingway leaves no doubt that the man is the manipulative antagonist of this story.
Sean already spoke to this. Listen to Sean. Sean is brilliant.
referred to as 'the man' or 'the American' not giving him an identity
Use regular quotation marks. Single quotation marks are only used to offset a quotation that is contained within material that is already in quotation marks.
The author makes the man out
to be very selfish
that he will to put up with the hassle of the baby ,but cares nothing about the baby.
Revise this. Your words are getting jumbled.
Ack! That is all I can do. I need to get onto my own homework and get into bed at a decent hour. Good luck with it!