This is because September used to be the seventh month. March was the new year and coinsided with spring planting, the spring equinox. At some point we switched from a solar calendar to a lunar one and that's when the new year month changed. Source for all this is the dead sea scrolls, see the book "Ancient Mysteries of the Essenes" for a deep dive on our calendar.
I thought the reason is because they added two months named July and August after emperors, which offset all the numbers by 2. (Sept, Oct, Nov, Dec - 7, 8, 9, 10)
That happened later, well after January and February had been added. I think the twelve month Roman calendar was from pre-history so we don't know when or why it was done. July and August were Quintilis and Sextilis, five and six.
All of the months with numerical prefixes are wrong by the same offset, though. So as long as you remember that as well, it can be useful. Particularly since they're the last ones and thus take the longest to count to.