This expression refers to the practice of “speaking out of both sides of the mouth” – shading the meaning of one’s words to appeal to a particular person or group, while purposely giving a different impression to others. In Japan, as elsewhere, this practice (though common) is considered duplicitous and hypocritical.
(Style: spoken/casual/A=female, B=male)
A: Iyaa, chigau naa. Kono aida no kaigi de wa sonna koto wa ittenakatta naa.
B: Soo kashira. Kyoo no ohanashi o sono mama tsutaeta dake da kedo.
A: Saikin, Mori-san nimaijita o tsukau yooni natte kita ne. Hanashi ga dondon kawaru n da kara tamannai yo.
A: No, that’s not it. He didn’t say that in the meeting the other day.
B: Really? I’m just reporting to you what he said to me today.
A: Mori has recently gotten into this habit of speaking from both sides of the mouth. His story changes from minute; I can’t stand it!