Why does the gemara bring the Azhara of Motzi Shem Ra from Lo Selech Rachil and not from Lo Sonu?
Although Ona'as Devarim means that it is prohibited to make one feel bad, it only applies only when making a remark to their face that embarrasses them (RAMBAM, Hilchos Teshuvah 7:10). Motzi Shem Ra applies whether or not the woman is present.
In addition, it could be that the Pasuk "Lo Selech Rachil" includes an inference to Motzi Shem Ra, since it ends "b'Amecha," a word reserved in other places for a wife (Lo Yitamei Ba'al b'Amav ). The other verse, "v'Nishmarta mi'Kol Davar Ra" mentions Dibur Ra, which certainly imples Motzi Shem Ra.
The verse you mentioned, though, mentions "Ish ba'Amito," which certainly does not sound like a man against his wife.