Being fired is a decision not a debate
If you are ever fired sit there and take the pain. Don't try to get your job back because your name was off of the payroll before they gave you the bad news.
The only way you should put up an argument is when and if you are fired for something you didn't do. That happened to me.
Instead of arguing with them and if the situation is really not your fault take it to the state labor board.
I was accused of making negative racial statements after I mistakenly referred to Black history week as African history week.
After I got fired I took the situation to the labor board and while I didn't get my job back I had the satisfaction of making them look stupid and I was able to collect unemployment.