The Matrix 2 and The Matrix 3 are huge R-rated movies.
Why did the Wachowskis choose to release these two movies in the same year?
I think the Matrix series is the only series which released two movies in same year.
The Matrix 2 and The Matrix 3 were filmed together (or "back to back").
Prior to the filming of The Matrix 2 and The Matrix 3, this was a pretty uncommon practice but did occur. In recent years it has become much more commonplace when it is known there will be multiple movies.
Release dates of movies filmed together have spanned anywhere from 3 months to 3 years apart (although Superman’s release was delayed due to staff differences rather than being planned that way).
Here is a, probably not comprehensive, list of movies filmed together with the intent of separate releases) along with their release dates (list courtesty of Wikipedia - missing dates added via google search):
As a result, while your question asks why (which I haven't answered), it also gives the basis that this is unusual where that seemingly is not the case. And unless the producers/directors/film company stops by to inform us, it would just be speculation.
But since you asked, my guess is that the decision is based primarily on which release cycle is estimated to bring in the most money.
Well, the second answer on a similar question on Quora says this:
Originally, the Wachowskis wanted to release The Matrix Reloaded in May and The Matrix Revolutions in June. This release schedule may have helped the perception of the sequels, as they were really one large movie, split in two. By the time November came around, the good will the third part may have had was gone, thanks in large part to critics not understanding the film.
Unfortunately, there is no citation. If true, this suggests from a story telling point of view, the Wachowskis wanted to have as small a gap as possible between releases.