The word fray is all about friction. A frayed rope has been rubbed so much its fibers are wearing away. People experiencing friction are involved in a fray, or a noisy fight.
If you have had a long day and feel like you're about to break down, you might say you are frayed. If students are arguing in class about whether nature or nurture is to blame for human problems, a teacher might stay out of the fray, letting the students reach their own conclusions.