Is the story "Hills like White Elephants" told objectively?
The story appears to be told objectively, but is it? What indication do you see of a narrator? Does the narrator seem to be male or female? Is there any sign that the narrator is judgmental of either or both of the characters? Look in particular at the word "reasonable."
You have asked more than one question and so I have edited it down to what enotes allows. When we consider this story what is highly interesting is the fact that it is almost entirely told through dialogue alone - the narrator has a very minimal role, and never comments directly on the conversation between the two characters and what is going on in their heads. Therefore we, as attentive readers, need to try and read between the lines to discover what is going on but also try to work out where the narrator's sympathy lies, if it lies anywhere at all.
However, having said this, I think the reader feels more sympathy for the girl than for the man. Note the insistence with which he keeps on making her consider the abortion, and in the end, note how she responds:
"Would you please please please please please please please please stop talking?"
It is clear that she feels pushed into a corner and has to decide between keeping the relationship or keeping her child. Reading between the lines reveals the pressure that the man is placing her under and the impossible position the girl is in. Therefore the use of the word "reasonable" is somewhat ironic, for it is the male who is not being reasonable in his repeated insistence that his girlfriend gets an abortion.