This is an excellent question. What is remarkable about this great short story is the way that so much is reported through the characters' dialogue alone - there is very little authorial intervention, and when the omniscient narrator does speak, it is only to report things that happen - we do not receive information what the characters are really thinking and what is going on inside of them. Thus we have to be careful readers and, like a detective, piece together what is happening.
It is clear that overtly at least the man appears to be very reasonable in his tone and diction:
"It's really an awfully simple operation, Jig," the man said. "It's not really an operation at all."
"I know you wouldn't mind it, Jig. It's really not anything. It's just to let the air in."
However, in spite of this dialogue, note the way that Jig, the girl, responds. She is silent and looks elsewhere, trying to ignore what he is saying. As you read the rest of the story it is clear with the insistence that the man keeps on bringing this up that it is he who is being completely unreasonable. He basically emotionally manipulates Jig into getting an abortion and forces her into a position where she has to chose between him and her unborn baby. This is why Jig threatens to scream and asks him to shut up towards the end of the story.
Reasonable therefore is not an adjective I would apply to the man - he demonstrates typical male supremacy in the way he gets what he wants and ignores the feelings of Jig.