- Is a Gezeirah Shavah known only through tradition passed down i.e. Torah She'Ba'al Peh? If so, then what is the hava amina that this Gezeirah Shavah is an explicit source for hilchos Chagigos?
Avraham Sacks, Ramat Beit Shemesh
1) Yes, the Gemara in Nidah 19b states that a person cannot make a Gezeirah Shavah on his own. Rashi explains that he must have received it from his teacher.
2) It seems to me that in Chagigah 10b, the Havah Amina might be that it is possible to have a Gezeirah Shavah if one word is in the Torah and the other word is in Navi. What we learn from the conclusion of the Gemara here is that if someone will come and claim that he received a Gezeirah Shavah from his Rebbi, where one word was from the Torah and the other word from the Nevi'im, we will inform him that this is not a legitimate Gezeirah Shavah.
3) I would just point out that not everything that looks like a Gezeirah Shavah is actually a Gezeirah Shavah. We find this in a different context in Tosfos (Erchin 15a, DH Havu), who writes that even though the Gemara there calls something a Gezeirah Shavah, it is not actually a full-scale Gezeirah Shavah. I would suggest that, according to this, it certainly would be possible to say that since the Gemara in Chagigah 10b never explicitly calls this a Gezeirah Shavah, even in the Havah Amina, this can mean that the Gemara never thought it was a proper Gezeirah Shavah but merely a "Giluy Milsa b'Alma": whenever we find the word "Midbar" connected with "Yachogu," this means that Zevachim are involved.
Kol Tuv,
Dovid Bloom