Why the difference between our Nisan 14 and Judaism's Nisan 14?

 Wol.JW.org

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• Some have noted, though, that this may differ from the date when Jews hold their Passover. Why?

  21 The Hebrew day ran from sunset (about six o’clock) to the next sunset. God commanded that the Passover lamb be killed on Nisan 14 “between the two evenings.” (Exodus 12:6) When would that be? Modern Jews cling to the rabbinical view that the lamb was to be slaughtered near the end of Nisan 14, between the time when the sun began to descend (about three o’clock) and the actual sunset. As a result, they hold their Seder after sundown, when Nisan 15 has begun.​—Mark 1:32.

  22 We have good reason, however, to understand the expression differently. Deuteronomy 16:6 clearly told the Israelites to “slaughter the passover sacrifice, in the evening, at sundown.” (Jewish Tanakh version) This indicates that “between the two evenings” referred to the twilight period, from sunset (which begins Nisan 14) to actual darkness. The ancient Karaite Jewsb understood it this way, as do Samaritansc down to today. Our accepting that the Passover lamb was sacrificed and eaten “at its appointed time” on Nisan 14, not on Nisan 15, is one reason why our Memorial date sometimes differs from the Jewish date.​—Numbers 9:2-5.

  23 Another reason why our date may differ from that of the Jews is that they employ a predetermined calendar, which system was not fixed until the fourth century C.E. Using this, they can set dates for Nisan 1 or for festivals decades or centuries beforehand. Moreover, the ancient lunar calendar needed to have a 13th month added occasionally so that the calendar would synchronize with the seasons. The current Jewish calendar adds this month at fixed points; in a 19-year cycle, it is added to years 3, 6, 8, 11, 14, 17, and 19.

  24 However, Emil Schürer says that “at the time of Jesus [the Jews] still had no fixed calendar, but on the basis of purely empirical observation, began each new month with the appearance of the new moon, and similarly on the basis of observation” added a month as needed. “If . . . it was noticed towards the end of the year that Passover would fall before the vernal equinox [about March 21], the intercalation of a month before Nisan was decreed.” (The History of the Jewish People in the Age of Jesus Christ, Volume 1) The extra month thus comes in naturally, not being added arbitrarily.