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I was about to comment on how this is because July and August were added in honor of Julius and Augustus Caesar, but it turns out they were renamed from Quintilis and Sextilis (which would also be misnumbered). It was really January and February that were added later, causing the off-by-2 error :)

Source: https://www.crowl.org/Lawrence/time/months.html

Now thank you for that... I wasn’t aware of this, but will probably never forget it again. You ruined these months for me! :-)

So we have the solution! Just put them back in their original order and call every other month N-ember!