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A new school year in Japan begins in April and since Bleach began in Mid-May then Ichigo had jsut started a new grade. Ichigo was stated to be a high school student in the first chapter:
Ichigo should be in 10th Grade at the start of the manga.
In Japan, a student in 10th Grade turns from 15 to 16 so it was planned from the start assuming Kubo had Ichigo's birthday planned out from the start. Looks like there was just a minor miscalculation on Kubo's part.