I didn't study Latin, but I can recognize when a noun is singular or plural.
It's weird that date is used in the singular form data in Portuguese - a Neo-Latin language - while Dutch contains the form I'd say makes more sense, datum.
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Italian, Spanish, Portuguese (etc.) data, and French date (whence English date) are all taken from Mediaeval Latin data, the plural of classical Latin datum, but reinterpreted in these languages as a singular noun. German and Dutch use the classical singular form datum.
All of these are bookish borrowings from Mediaeval or Classical Latin (so-called cultisms) and not organic descendants of the Latin words.
There's probably no straight answer, why this happened in two languages. Here's just one hypothesis that may give a good start.
The etymology of "date" in English (and, likely, in other European languages) is:
The Roman convention of closing every article of correspondence by writing "given" and the day and month -- meaning perhaps "given to messenger" -- led to data becoming a term for "the time (and place) stated."
A Roman letter would include something along the lines of datum Romae pridie Kalendas Maias -- "given at Rome on the last day of April."
As we see, the assumed full sentence is something like:
"This message is given on [day, month, year, and place]."
"The message" is singular, hence, "datum".
It is easy to suppose that "this message" may at some languages/areas change its meaning slightly: "these statements are given…" or "these scripts are given…", both plural, hence, "data".
Since the difference is very slight, it can be supposed that singular/plural variants may cycle, even in the same areas.