Jewish Calendar

I have a question. I don't understand 2 things. First, why did the Jews begin the 490 years countdown of Daniel 9:24-27 when the first temple was destroyed (Jewish calendar 424/422BC or Gentile date 586 BC) instead of the "decree" of say Cyrus or another figure in Daniel's immediate future to rebuild (536 BC or so)? Is there something in the Hebrew I'm missing? Secondly, I don't understand why or how the Jewish calendar for the date of the destruction of the Temple is so different in the Jewish calendar than the Gentile one - a difference of 164 years or so. I understand that there is roughly 490 years from the destruction of the first temple to the second in AD 70 based on the Jewish calendar (and that is how you understand the 490 years), but I don't understand why the 490 years begins at the destruction of the first temple and not with Cyrus, and I don't understand why the Jewish calendar is 165 years off from the other. Any help would be appreciated.