It is a widespread minhag (Kitzur Shulchan Aruch 78:4, though by no means do all communities do this) that during the Tochachah of Bechukosai (Vayikra 26) and Ki Savo (Devarim 28), the reader reads this section quietly and quickly.
Nevertheless, the Midrash (Koheles Rabbah 8:7 in Warsaw numbering) notes that some Amoraim disapproved of this practice (translation follows Eitz Yosef and Matnos Kehunah):
רבי לוי בן פנטי קרא את ארוריא קדם רבי הונא וגמגם בהון אמר ליה אשמע קליך דלית אינון קללות תוכחות אינון
R’ Levi ben Panti read the curses before R’ Huna, and he mumbled them. He said to him: Let me head your voice, for they are not curses; they are rebukes.
R’ Huna clearly held that we should not mumble during the Tochachah (as an inspiration to do Teshuvah - Yefeh Anaf). Granted that we don’t necessarily pasken a Midrash, but what is wrong with his logic that many have the minhag not to follow it?
It is unclear to me whether R’ Levi accepted R’ Huna’s opinion. If anyone can prove to me that R’ Levi continued this practice in spite of R’ Huna’s psak, perhaps we could argue that we follow R’ Levi.
In respect to the line opening by saying he was reading the “curses” - while that is Artscroll’s translation, Eitz Yosef translates it as “rebuke.”