The central conflict in Irwin Shaw's "The Girls in Their Summer Dresses" exists between Michael Loomis and his wife of five years, Frances.
A conflict is "the struggle between opposing forces." The two forces here are Michael and Frances. As the couple walks along one November day in New York City, Frances comments on the fact that Michael is watching the women that pass by. This is not something new. Obviously Frances has noted this habit for a very long time, but it is now being addressed by Frances as they walk.
The noticeable conflict is that Michael watches other nice-looking women. This makes Frances feel extremely self-conscious and sad, even though she is still a beautiful woman. However, Michael also is demonstrating his lack of regard for his wife and a sense that he is entitled to do what he chooses. In fact, he refuses to admit if he is right or wrong, and he tries to blame his truthful declarations on Frances:
"I look at women," he said. "Correct. I don't say it's wrong or right, I look at them. If I pass them on the street and I don't look at them, I'm fooling you, I'm fooling myself."
When Frances accuses Michael of wanting these women he says:
"Right," Michael said, being cruel now and not caring, because she had made him expose himself. "You brought this subject up for discussion, we will discuss it fully."
Michael cares more about his own pleasures than the feelings of his wife. This realization (which may not be completely unsuspected by Frances) hurts her deeply. And as the story goes on, we understand that Frances loves Michael, though it may be in a much too grasping and desperate way that makes her husband unhappy: in fact, he may be pulling away because she exhibits a sense of desperation that Michal cannot live comfortably with.
I think the theme of the story is purily jelousy