argue one's case [meaning]

[csicska]

Hello. Could you please paraphrase for me what the phrase "argue one's case" means? Does it mean "to give reasons for or against 'the case' in order to change someone's opinion about 'the case'"?
Can I use it, for example, as follows?

My professor gave me the detention because he thought that I cheated on the exam but I was trying to argue my case (i.e. "the case" here would be the detention given and I could argue my case e.g. in the following way: "Professor, why are you giving me a detention? You said that I cheated using the cell phone while I only checked it to see how much time there was left. Moreover, this old type of a cell phone does not support the storage of files nor does it allow to connect to the Internet." - in this case, I would be arguing against 'the case')

My professor did not allow me to sit next to window because he said I would be throwing things out of it. (i.e. "the case" here would be "sitting next to the window" and I might argue my case, for example, in the following way: "Professor, I participate in the public litter removal. Moreover, I need sun rays for my life." - in this case, I would be arguing for 'the case')

Do I understand the phrase correctly? Thank you.

 

[Thomas Tompion]

I'm not sure you do, Csicska.

To argue one's case is to have a point of view and present it with vigour and, one hopes, logic.

It doesn't necessarily include considering the arguments against one, except for the purpose of dismissing them.

 

[csicska]

Thank you, Thomas Tompion.

So the "vigor and enthusiasm" is what differs the phrase "to argue one's case" from a plain "to state one's opinion"?

 

[Thomas Tompion]

Not entirely. You mustn't forget that little bit about logic.

You won't persuade people if you simply state your opinion without justifying it with arguments.

 

[csicska]

Thank you. I think I am able to see the meaning and the difference from the plain "stating of one's opinion" now.