Why is JD 2451545.0 = January 1, 2000, Noon instead of JD 2451558.0?
This Wikipedia article states (correctly) that


  "The Julian Day Number (JDN) is the integer assigned to a whole solar
  day in the Julian day count starting from noon Greenwich Mean Time,
  with Julian day number 0 assigned to the day starting at noon on
  January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC,
  in the proleptic Gregorian calendar)"


The Julian year consists of 365.25 days while a Gregorian year consists of 365.2425 days.  

Since the introduction of the Gregorian calendar, the difference between Gregorian and Julian calendar dates has increased by three days every four centuries (all date ranges are inclusive).  In addition, 10 days were added to the Julian calendar to obtain the Gregorian calendar at the time of the calendar reform. The current difference between the Gregorian and Julian calendar dates is 13 days: 14 September 2016 Gregorian date is 1 September 2016 (Julian date).

This should explain the extra 13 days in your calculations.