Importance of Name Who Authored each Mishna

Hi Rabbi. The question is why the Gemara often spends time on working out who wrote a Mishna or a Braita? The answer I thought of was that each Rabbi has a different level of authority and some Rabbis opinions are stronger than others. The problem I had with that was that it becomes an appeal to authority fallacy in a logical argument. Am I right in my understanding of the reason for finding the author? If Im wrong, what is the actual reason for it?

There definitely is truth in what you wrote regarding the importance in knowing the authorship of each Mishna/Braita, for there are very clear rules in halacha regarding certain tannaim, whose halachic and logical (!) "clout" and authority were universally accepted, generally based upon their outstanding knowledge, number of students, etc. For example, halacha is always like R. Eliezer ben Ya'akov- even against many tannaim; like R. Yehoshua vs. R. Eliezer; like R. Yehuda haNasi if he disagrees with 1 tanna but not if there several who oppose him, etc. In addition, and even more basic: the Oral Tradition is, for obvious reasons, based upon exact transmission, which is a "safety" against inaccurate passage (especially before the printing press!), and includes the exact details of each and every statement, including who exactly said what.