Your memory of a conversation includes sentences the other person may not remember saying.

Memory is reconstruction, not recording. You keep the gist and rebuild the rest each time, filling in with what would have made sense, so lines get sharpened, motives get clarified, and the other person ends up having said something they would not recognise. Neither of you is lying when your accounts differ. You are both remembering normally.

In a disagreement about what was said, try treating both versions as partly built rather than one as false. Ask what the other person understood at the time. That question moves things forward when arguing about the transcript never does.