The first is in Sanhedrin 109b, and deals with Korach who was הקהה the teeth of his forebears. This relationship to parents in this context appears a reversal of the imagery in Yirmeyahu, where the fathers eat and the sons have their teeth affected.
תלמוד בבלי מסכת סנהדרין דף קט עמוד ב
קרח - שנעשה קרחה בישראל, בן יצהר - בן שהרתיח עליו את כל העולם כצהרים, בן קהת - בן שהקהה שיני מולידיו, בן לוי - בן שנעשה לויה בגיהנם.
קרח - שנעשה קרחה בישראל, בן יצהר - בן שהרתיח עליו את כל העולם כצהרים, בן קהת - בן שהקהה שיני מולידיו, בן לוי - בן שנעשה לויה בגיהנם.
What does this mean? Weaken? Break? Set on edge? I don't know, but given that they were probably displeased with these actions, and were disgraced by them, "set on edge" makes sense. As Soncino translates:
Now Korah took …8 Resh Lakish said: He took a bad bargain for himself, being plucked out9 of Israel. The son of Izhar: a son who incensed10 the whole world with himself as the [heat of] noon.11 The son of Kohath,12 a son who set the teeth of his progenitors on edge.13 The son of Levi: a son who became an inmate14 of Gehenna.And as Rashi explains there:
Does "blunt the teeth" make sense? Perhaps.רש"י מסכת סנהדרין דף קט עמוד ב
הקהה שיני מולידיו - שנתביישו אבותיו במעשיו הרעים.
Another instance of this idiom is in Sotah 49a. Here Soncino is inconsistent and renders it "blunt the teeth."
תלמוד בבלי מסכת סוטה דף מט עמוד א
שמבזבזין דין אביהם לעתיד לבוא, אומרים לפניו: רבונו של עולם, מאחר שאתה עתיד ליפרע מהן, למה הקהיתה שיניהם בם! אמר ר' אילעא בר יברכיה: אלמלא תפלתו של דוד - היו כל ישראל מוכרי רבב, שנאמר: +תהלים ט+ שיתה ה' מורה להם. וא"ר אילעא בר יברכיה: אלמלא תפלתו של חבקוק - היו ב' תלמידי חכמים מתכסים בטלית אחת ועוסקין בתורה, שנאמר: +חבקוק ג+ ה' שמעתי שמעך יראתי ה' פעלך בקרב שנים חייהו, אל תקרא בקרב שנים אלא בקרוב שנים ואמר ר' אילעא בר יברכיה
AND MEN OF FAITH DISAPPEARED. R. Isaac said: These are men who had faith in the Holy One, blessed be He. For it has been taught: R. Eliezer the Great40 declares: Whoever has a piece of bread in his basket and Says. 'What shall I eat tomorrow?' belongs only to them who are little in faith. And that is what R. Eleazar said: What means that which is written: For who hath despised the day of small things?41 [It signifies,] What is the cause that the tables of the righteous are despoiled in the Hereafter?42 The smallness [of faith] which was in them, that they did not trust in the Holy One, blessed be He. Raba said: They are the little ones43 among the children of the wicked of Israel who despoil the verdict upon their fathers in the Hereafter, Saying before Him, 'Sovereign of the Universe! Since thou art about to exact punishment of them, why hast Thou blunted their teeth?'1Where the reference of "blunting their teeth" is to the death of the children. Nothing in particular about this tells me what the meaning is. "Set teeth on edge" suggests to me some sort of shock. But blunt/break there teeth can also work, I suppose. And Soncino chooses it here, for some reason.
A bit later on the same daf:
תניא ר"ש בן אלעזר אומר טהרה בטלה טעם וריח מעשר ביטל שומן דגן רב הונא אשכח תומרתא דחינוניתא שקלה כרכה בסודריה אתא רבה בריה א"ל מורחינא ריחא דחינוניתא א"ל בני טהרה יש בך יהבה ניהליה אדהכי אתא אבא בריה שקלה יהבה ניהליה א"ל בני שמחת את לבי והקהיתה את שיני היינו דאמרי אינשי רחמי דאבא אבני רחמי דבני אבני דהוו ליה רב אחא בר יעקב איטפל ביה ברב יעקב בר ברתיה כי גדל א"ל אשקיין מיא אמר לו לאו בריך אנא והיינו דאמרי אינשי רבי רבי בר ברתך אנא:
THE DEW HAS NOT DESCENDED FOR A BLESSING AND THE FLAVOUR HAS DEPARTED FROM THE FRUITS etc. It has been taught: R. Simeon b. Eleazar Says: [The cessation of] purity has removed taste and fragrance [from fruits]; [the cessation of] tithes has removed the fatness of corn. R. Huna once found a juicy date which he took and wrapped in his mantle. His son, Rabbah, came and said to him, 'I smell the fragrance of a juicy date'. He said to him, 'My son, there is purity in thee',22 and gave it to him. Meanwhile [Rabbah's] son, Abba, came; [Rabbah] took it and gave it to him. [R. Huna] said to [Rabbah], 'My son, thou hast gladdened my heart23 and blunted my teeth'.24 That is what the popular proverb Says, 'A father's love is for his children; the children's love is for their own children.Did he blunt the teeth because he displayed more love for his son than for his father, if he was not going to eat it anyway? Or is this intended in some literal manner, that the teeth were blunted in that he was not allowed to eat the date? Once again, this could mean either of the two ("set on edge" vs. "blunt"), and I don't really see a basis for choosing one over the other.
Forget about which of these two. Can we transfer this meaning to the haggadah? Perhaps. הקהה את שיניו seems in these cases to be non-literal, just as we would expect. And it means to cause someone some emotional hurt. Thus, Korach did this to his progenitors via his action, God did this to the wicked by taking away their children, and Rabba did it to Rav Huna by showing more concern for his son than for his father.
Similarly by the Haggadah, the forceful answer with be hurtful to the wicked son.
We should perhaps check what meforshim say on these gemaras, to get a better sense of what they see as the meaning, and such that we may revise our opinion as well. Next up, the midrash Rabbah.