How can there be machlokes in gezairah shavos?

Question

The Gemara says (Nidah 19b, among other places), אין אדם דן גזירה שווה מעצמו - a person can't make up gezaira shavos, they have to have been learned from one's teacher. If so, how can there ever be a dispute regarding them?

Answer 1

I think this question is sort of addressed by the Gemara in Megillah 2b with Rashi's explanation.

מתני' דלא כי האי תנא דתניא רבי יהושע בן קרחה אומר כרכין המוקפין חומה מימות אחשורוש קורין בחמשה עשר מ"ט דרבי יהושע בן קרחה כי שושן מה שושן מוקפת חומה מימות אחשורוש וקורין בחמשה עשר אף כל שמוקפת חומה מימות אחשורוש קורין בחמשה עשר ותנא דידן מ"ט יליף פרזי פרזי כתיב הכא על כן היהודים הפרזים וכתיב התם לבד מערי הפרזי הרבה מאד מה להלן מוקפת חומה מימות יהושע בן נון אף כאן מוקפת חומה מימות יהושע בן נון בשלמא רבי יהושע בן קרחה לא אמר כתנא דידן דלית ליה פרזי פרזי אלא תנא דידן מ"ט לא אמר כר' יהושע בן קרחה מ"ט דהא אית ליה פרזי פרזי הכי קאמר אלא שושן דעבד' כמאן לא כפרזים ולא כמוקפין אמר רבא ואמרי לה כדי שאני שושן הואיל ונעשה בה נס

Our Mishnah does not take the same view as the following Tanna, as it has been taught: ‘R. Joshua b. Korha says: Cities which have been walled since the days of Ahasuerus read on the fifteenth’. What is the reason of R. Joshua b. Korha? — [They must be] like Susa: just as Susa has been walled since the days of Ahasuerus and reads on the fifteenth, so every city that has been walled since the days of Ahasuerus reads on the fifteenth. What then is the reason of our Tanna? — He draws an analogy between the two occurrences of the word perazi [villagers]. It is written here, Therefore the Jews of the villages [ha — perazim], and it is written in another place, beside the unwalled [ha — perazi] towns, a great many; just as there the reference is to towns which were [not] walled in the days of Joshua son of Nun, so here the reference is to towns which were [not] walled in the days of Joshua son of Nun. I can understand why R. Joshua b. Korha did not adopt the view of our Tanna; he does not accept the analogy of perazi and perazi. But why does not our Tanna accept the view of R.Joshua b. Korha? — [You ask] why does he not? Why, because he draws the analogy of perazi with perazi, of course! What the questioner meant was this: [On the view of our Tanna], whom did Susa follow? It followed neither the villages nor the walled towns! — Raba, or, as some say, Kadi, replied: Susa was an exception, because a miracle was performed in it.

Rashi there explains:

לא גמיר גזירה שוה מרביה ואין אדם דן גזירה שוה מעצמו אלא אם כן קיבלה מרבו

He had not learned this gezeirah shaveh from his teacher, and a person cannot judge a gezeirah shaveh on his own unless he received it from his teacher.

Answer 2

The Shitta Mekubetset to Bava Metsia (87b) quotes Ramban, Rashba, and Ran who write that the tradition only included which words were involved in the g'zera shava, but not what the g'zera shava taught. This deals with cases in which they argue about the content of the derasha, but not cases where one dismisses the derasha entirely. (The question seemed open ended; including both cases).

It is also possible that a given derasha is meant as more of an asmakhta for a rule that the expounder already holds of. Indeed, in the Yerushalmi Pesahim (6:1), the teaching that one does not make a g'zera shava himself is taught by R. Yossi bar Bun in the name of R. Abba bar Mamal, and he himself states that a person can make a g'zera shava to support his teaching:

ר' יוסה בי רבי בון בשם רבי בא בר ממל אדם דן גזירה שוה לקיים תלמודו ואין אדם דן גז"ש לבטל תלמודו. רבי יוסי בי רבי בון בשם ר' בא בר ממל אדם דן ק"ו לעצמו ואין אדם דן גזרה שוה לעצמו לפיכך משיבין מק"ו ואין מושיבין מגזרה שוה

The Korban HaEdah there (s.v. Adam Dan) explains that in a case where someone has a tradition about a law, one can then make his own g'zera shava to support it:

אדם דן גזרה שוה. מעצמו לקיים תלמודו שקיבל מרבו דאין הפסד בדבר שהרי בלאו הכי הדין כן ואין גזרה שוה זו אלא לסמוך בעלמא

Alei Tamar to Yerushalmi Kilayim (9:1) uses the aforementioned Yerushalmi to explain cases of g'zera shava involving words in Nakh. Obviously those weren't Sinaic, so at some point somebody made it up. These are okay, however, since such a case isn't an actual g'zera shava, but a mere rabbinic asmakhta. He doesn't specify that a tradition for the given halakha is necessary.

This would address even cases in which there is a dispute over whether a g'zera shava between two words exists at all.