Let us examine this verse and open with an initial question. Why did Judah choose to speak in such a harsh tone to Joseph that he even had to make a disclaimer saying please don't get angry due to my tone. Aren't we taught that the words of wise men should always come across in tranquility and calm!?
Additionally upon further analysis, why does Judah say to Joseph "יְדַבֶּר־נָ֨א עַבְדְּךָ֤ דָבָר֙" 'Let your servant speak to you this thing', he should have just said 'Let your servent speak to you'.. why this extra wording of davar/thing within his request to talk?!
And it seems that to answer our questions, with the help of Heaven, we first have to understand that Joseph in this scenario was acting with total justice. Even furthermore knowing that he was more righteous and fair compared to Judah's claim of Joseph acting unreasonable in this scenario. Didnt Judah himself bring this situation on himself when he proclaimed the following -
So how could Judah complain that Joseph is being unreasonable and unfair when Judah himself proclaimed what the punishment should be, as seen above!? And after all this Joseph was simply seeking to punish the one who had the stolen goblet in his possession, which would be Benjamin. And on such a fitting and fair judgement set in place by Joseph, Judah didn't open his mouth to question the judgement, and furthermore it was the case that Judah did indeed speak with calmness to Joseph (We thought he didn't because of the verse where Judah tells Joseph 'don't be angered by my tone' which would imply he spoke harshly).
We actually see this to be true based on the following Medrash -
So it seems that Judah actually did talk gentle to Joseph like a wise man should, however he knew that even if he speaks in a relaxed and pleasant tone to Joseph, that Joseph would still be angered by his audacity to question his fair judgement, therefor he said please don't be angered by my words as a precaution even though he did speak gentle.
If this is the case (That Judah spoke gentle and was already in acceptance of Josephs fair judgement) then we must understand what Judahs claim really was! There is an opinion to suggest that Judah was presenting a totally new claim to Joseph of why this isn't fair. He was speaking in line with Josephs rationale of punishment using Josephs logic (which was that only the offender should be punished) in order to actually have Benjamin freed.
Behold, it is taught in the Holy text Agra D'Parka -
(Tzvi Elimelech Spira of Dinov (1783–January 11, 1841) was a famous Hasidic Rebbe in Poland. He was a nephew of Elimelech of Lizhensk, and was a prolific writer, known as the author of Bnei Yissachar)
He writes the following based on the below verse -
Based on this verse from King Solomon, the sages expound and teach the following -
We have to understand here what effect does relating your suffering to others have on your unfortunate state that it helps lower it.
The answer is as follows - When G-D forbid an unfortunate suffering befalls upon you, or some sort loss, or fear from the haters of Israel. The person receiving the suffering suffers the most from the actual scenario, however his relatives, loved ones, and friends also suffer due to his suffering, each one more or less based on how much they love or are close with him.
And behold, if he sins and brings certain suffering upon himself, what sin did his loved ones and relatives do that they now have this suffering come upon them on behalf of their friend! It would be impossible to suggest that there is a perversion of divine justice based on the fact that they are suffering for no reason due to the sin of their loved one who actually did do something and did deserve such suffering. Because by default we have a reality that there is no perversion of justice with G-D as we can see from the following verse -
Therefor, at the time when an unfortunate suffering G-D forbid falls upon a person his relatives and loved ones are doomed in that each one to his/her own degree feels this suffering as well, so then this punishment descends upon and is accepted by all that it effects as if they deserved it too. However, if there is someone in his family who really isn't deserving of any suffering from a heavenly judgement perspective, then this person by default will save the original guy who is suffering and deserved it, this is because through the suffering of a righteous person, his loves ones suffer, since HaShem doesn't pervert judgement and make people suffer who aren't deserving. And this is the meaning behind the above advice to tell other people your suffering based on the above verse in Proverbs - 'If there is anxiety in a man’s mind let him quash it, and turn it into joy with a good word.'
Perhaps you will find someone who is not deserving of any suffering, who will enter into a state of suffering once hearing about your suffering (since he feels bad), and then by default HaShem will have to remove the suffering from the original sufferer, as to not make this righteous friend of his suffer based on your suffering.
Until here are his words.
And based on this, it's possible to say that this is the specific claim Judah was making to Joseph, as he says let your servant talk to you regarding this thing. Which means that Judah was telling Joseph 'let me interject here and suggest a new logic, into your ears', something that will enter your ears specifically, that according to your rationale Joseph, that only the sinner here should be punished and no one else, on that you should know that your punishment is also falling upon those that didn't sin! Since the boys father's soul is tied up with the soul of this boy, and he will be extremely distraught on losing his son! As well, upon me punishment will fall, since your servant (myself) took responsibility/guarantorship on this boy...
"This is a correct understanding with the help of Heaven. After weaving this together I had found something in the same light written by the first Lisker Rebbe (circa 1850's) in the Holy text 'Ach Pri Tevua'"