The answer I think is like this:
At the conclusion (with R' Huna), the halacha is established like R' Eliezer ben Yakov, hence the case with gifting the father the barrels of wine must be compatible with R' Eliezer ben Yakov. And the only option to do that was with dog theory, so therefore R' Eliezer ben Yakov must hold of dog theory. Apparently nothing else can establish apples and oranges for R' Eliezer ben Yakov.
R. Eliezer ben Yakov agrees whenever one could say "I am not a dog" that it is a real vow
https://dafyomi.co.il/nedarim/tosfos/nd-ts-024.htm#:~:text=R.%20Eliezer%20ben%20Yakov%20agrees%20whenever%20one%20could%20say%20%22I%20am%20not%20a%20dog%22%20that%20it%20is%20a%20real%20vow
https://www.sefaria.org/Nedarim.24a.3?ven=William_Davidson_Edition_-_English&vhe=William_Davidson_Edition_-_Vocalized_Aramaic&lang=bi#:~:text=%D7%9C%D6%B0%D7%A2%D7%95%D6%B9%D7%9C%D6%B8%D7%9D%20%D7%A8%D6%B7%D7%91%D6%BC%D6%B4%D7%99%20%D7%90%D6%B1%D7%9C%D6%B4%D7%99%D7%A2%D6%B6%D7%96%D6%B6%D7%A8,means%20of%20encouragement.
Dog theory was only used as a conjecture to reject a proof that was shown to possibly not be bullet-proof. What right does Ran have to establish that as fact?!
In other words: Isn't this the most we are allowed to state:
Maybe R. Eliezer ben Yakov agrees whenever one could say "I am not a dog" that it is a real vow
Paul Davidowitz, Long Beach, NY, USA
1) Yes, the Ran on 24b (DH ul'Inyan) writes that in the conclusion we retracted from "I am not a dog" according to Rebbi Eliezer ben Yakov.
2) The Ran on 24a (DH Yeser A'K) writes that the answer of the Gemara, "I am not a dog," is a "Dichuya b'Alma" -- it is merely a "push-off" and is not the truth of the matter; it is a conjecture.
3) However, above on this Daf (24a, DH Mishum), the Ran writes that others say that there is a stronger reason to say "I am not a dog." This is because A gave a big present to B.
(I found cited that a "Kor" of wheat, mentioned on the second line of 24a, occupies a volume of 432 liters according to the Shitah of the Chazon Ish. Together with the two barrels of wine, this represents a substantial present)
The Ran writes that if A gives such a big present to B, then it makes sense that B will say "I am not a dog" and will demand that A will accept a gift from him in return. But it is not considered unusual for A merely to invite B for a meal, and therefore the argument of "I am not a dog" -- and thus B will demand that A should agree to be invited in return -- is weaker in this scenario.
4) The Ran (24b, DH ul'Inyan) writes that according to the Pshat that I cited above (that "I am not a dog" is merely a push-off), it follows that this does not make it a real vow. However, according to the Pshat that "I am not a dog" applies only to a substantial gift, it follows that "I am not a dog" does apply according to the conclusion of the Gemara if a big present was given.
5) It seems, therefore, that it is all or nothing. If we are discussing a scenario where A gave a big present to B, then "I am not a dog" is a powerful argument, but if he gave a small present to B, then "I am not a dog" is just a push-off of the Gemara.
6) So I think that we should rephrase the conclusion and it will not read:
"Perhaps Rebbi Eliezer ben Yakov agrees whenever one could say 'I am not a dog' that it is a real vow,"
but it should instead read,
"If it is a big present then it is a real vow but if it is a small present then it is not a vow."
Kol Tuv,
Dovid Bloom