Half-Baked Arguments
וּפְרוּסָה מַאי טַעְמָא לָא? אָמַר רַבִּי יוֹסֵי בֶּן שָׁאוּל אָמַר רַבִּי: מִשּׁוּם אֵיבָה.
The Gemara analyzes Rabbi Yehoshua’s position itself: And with regard to a broken loaf of bread, what is the reason that it may not be used for an eiruv? Rabbi Yosei ben Shaul said that Rabbi Yehuda HaNasi said: The reason is due to potential enmity between neighbors. To avoid a situation where one person says to the other: You contributed a mere slice of bread, while I donated an entire loaf, the Sages instituted that each person should provide a whole loaf.
Rashi
משום איבה - שבאין לידי מחלוקת שאומר אני נותן שלימה ואתה פרוסה:
Rabbenu Chananel
ופרוסה מ"ט לא משום איבה דאמר אמאי מייתינא אנא שלימה והאי פרוסה
Slight difference in language between Rashi and Rabbenu Chananel:
Rashi says there is potential for discord: The one who brought a whole loaf will complain to the one who brought the partial loaf, “I brought a whole loaf and you bring a broken piece?”
Rabbenu Chananel describes a situation that is not a direct confrontation, but rather the person who brought a whole loaf says to the other contributors, “Why did I bring a whole loaf and this OTHER guy brought only a broken piece?”
In effect, Rashi is describing an argument between two people while Rabbenu Chananel is describing l’shon hora and backstabbing.
Rashi’s idea of the problem is also echoed in Sanhedrin 110a
(במדבר טז, כה) ויקם משה וילך אל דתן ואבירם אמר ר"ל מכאן שאין מחזיקין במחלוקת דאמר רב כל המחזיק במחלוקת עובר בלאו שנאמר (במדבר יז, ה) ולא יהיה כקרח וכעדתו
With regard to the verse: “And Moses arose and went to Dathan and Abiram” (Numbers 16:25), Reish Lakish says: From here we derive that one may not perpetuate a dispute, as Rav says: Anyone who perpetuates a dispute violates a prohibition, as it is stated: “And he will not be like Korah and his assembly, as the Lord spoke by the hand of Moses to him” (Numbers 17:5). Even the aggrieved party must seek to end the dispute. Dathan and Abiram accused Moses and by right should have initiated the reconciliation. Nevertheless, Moses was not insistent on this; he went to them.
This Gemara implies a separate prohibition to cause quarrel. Most commentaries understand this to be an asmakhta, a rabbinic inference, and not a true commandment (see Torah Temima Deuteronomy 6:7 and 21:23) However, Ramban in his commentary on Rambam’s Sefer Hamitzvos (Siyum 3) counts לא יהיה כקרח as an explicit negative prohibition. Because actually the simple reading of the verse is prohibition against doubting leadership or perhaps rebelling against the divinely mandated privilege of the priesthood.
Perhaps we can say the machlokes Rabbenu Chananel and Rashi depends on if one considers causing discord to be a Biblical prohibition or not. Rashi will hold like Ramban, that Causing discord and strife is a Biblical negative prohibition, therefore this is the primary concern of our Gemara that allowing incomplete loaves would lead to strife. While Rabbenu Chananel holds there is no biblical provision, and therefore interprets this as a problem using incomplete loaves would lead to forbidden speech l’shon hora.
for Video Shiur click here to listen: Psychology of the DAF Eruvin 81
Translation Courtesy of Sefaria
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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