Whenever I have an argument or a fight with someone, I think like "fighting is totally different from having a conversation".
When two pepole are fighting, they are just claiming not listening to the other. = When two people are fighting, they don't want to hear the other person's side.

Finally, that makes them get exhausted.
Some people have kind of misunderstanding like having a conversation is sort of discussion.  = Some people have some sort of misunderstanding and it leads to conflict and resentment.

It's like in order to persuade the other, they are just expressing their own opinion to each other.  = It's like in order to persuade others, they try to express their own opinion. 

However in my opinion, I think it's wrong.

if = If either of them has uncomfable = uncomfortable feeling to the other, it is even more difficult to communicate.

Maybe they just keep try to persuade until the other say "you're right. I'm sorry".  = Maybe they just have to keep on trying to persuade her/him until he/she agrees. 

Does that way really work as well as thier thought? = Does that way really work?

Based on my experience, those poeple = people don't consider the other's feeling while they're claiming.

They are just thinking of themselves = They only think of themselves

and act like "I have more logical and reasonable opinion, but you don't. Why can't you think as what I'm thinking?". Those thoughts just make communication worse.

What they have to is just to stop talking and put themselves in the ohter's shoes. = What you have to do is to stop talking and try put yourself in other's shoes. 

They need to have time before delivering their opinions and throw away these thought like "I'm right and you're wrong". = They need to have time before expressing their opinions and stop being self-righteous.