These three phenomena are independent of each other, so there is no direct correlation between them.
Contrary to popular belief, Judaism does not maintain that Jews are better than other people.
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Clearly, these are not the ideas of a people who think they are better than other nations.
Because of our acceptance of Torah, Jews have a special status in the eyes of G-d, but we lose that special status when we abandon Torah.
Holidays are celebrated on the same day of the Jewish calendar every year, but the Jewish year is not the same length as a solar year on the civil calendar used by most of the western world, so the date shifts on the civil calendar.