In the conventional calendar, there wasn’t a year zero and it wasn’t skipped. Zero is the moment in time that we use to begin counting time.
Think of an elementary school style number line: …-3_-2_-1_0_1_2_3… Each number is one year apart. This makes the numbers measure something like Age. If you are 3 years old, you can count 3 years between 0 and 3.
But a year is not an Age. It is the span of time between ages, and the years we name are actually the spaces between the numbers on the number line. So the first year (1 AD/CE) is the first space after zero (between 0 and 1), and the first negative year (1 BC/BCE) is the first space before the 0 (between -1 and 0).
Then there is the astronomical calendar, which does have a year zero. They get this by naming the year (the space on the number line) after the number to the right side of the space on the number line.