Yedrin structures his lie very well, and he should, since he's had 200 years to think about it. Sisko hates the idea of never seeing his family again. To make Sisko more open to his plan, Yedrin other-izes the quantum copy of the crew and describes the version who carry on back to the station as "you." That makes Sisko feel certain that his consciousness will get to return to his family and not dwell on the fact that a quantum copy would also expect to be the "you" who gets to return home. Yedrin's lie also ensures that, when the crew does get sent back in time, they'll just assume that they are actually their quantum copies, keeping Yedrin's lie a secret.
