Why is it reasonable to believe that this student handed in a term paper from another class? I have a student who has handed in a term paper from another class, only changing the title page, and he claims that he only put the due date for the current course's term paper on the cover sheet of the old term paper to remind him of when the new term paper was due. He claims he was then cutting and pasting (appropriately, of course) between the old paper and the new paper and must've gotten the two files mixed up. Of course, the "wrong" file (old term paper with new due date) was "accidentally" uploaded to our learning management system and he did submit the "correct" file two days later (that was extremely poor quality), but only after I pointed out the problem to him. 

Now he is claiming I am unreasonable because I don't believe him and have failed him for the course. We are about to go to a grade appeal at the department level. I was wondering if everyone on here could provide suggestions for why it is reasonable to stick to my decision, despite the student arguing very vigorously that I'm unreasonable, unfair, and even irrational for not believing this was "just an honest mistake". (Given my university's fondness for "student friendly" I may not be supported very vigorously by the committee.)

Any help is greatly appreciated.
I might be having a completely different stance on the topic, however I feel it needs to be thought about. The primary goal of a school would be to asses whether the student in question has achieved a certain level of competences. 
In order to test those competences you'd give all sorts of assignments to see whether the student has both competences AND skills required for their studies.

As @Significance and @DanRomik mentioned before, filing the other paper can be seen as self-plagiarism. However, if you consider that filing this paper is invalid you could also say that he never filed any valid paper in the first place. Meaning he crossed the deadline that was given for this paper.

School is a place to prepare a person to work at companies and more. So it would not be a bad idea to treat a student as if he were an employee. He filed his work late, couldn't meet the deadline and would obviously be penalized. Now since school is a place to learn from your mistakes you could throw him a lifeline. Rather than smashing him down, I'd accept his paper that was of extremely poor quality, but penalize the grade of this paper based on crossing the deadline.

Now, in the end he may still fail due to the poor quality + crossed deadline. But at the very least he would have learned to be more punctual about his work. 

After all, being able to deliver good quality work on a timely way are some of the most important competences a student has to learn.