The literal translation is "Write the date of birth here." It does not say "Write YOUR date of birth here," although I will admit that it could be implied.
Why would you assume it's 'your' birthdate? It could be your child's birthdate.
In English this could be translated many ways that duo lingo does not accept. Ex. Write the date of your birth here
But it gives as an optional correct response "write down your date of birth here." If "your" is OK here, "the date of your birth" should also be OK. Reported.
I understand - write the date of birth here, where does the "down" come from?
Date of birth and birth date are the same and used interchangeably. Birthday also refers to date of birth but since the sentence said "data di nascita" you wouldn't use birthday
without context is there any reason why it must be "your date" instead of "date"?
I a previous sentence the right answer was "birth date". Here it is "birthdate". Why?