Translation:I need to take a day off today.
"I need to take today off" also rejected and that is the most natural English translation
I agree. It's just told me that the correct answer is "I want to take off today", which is something completely different.
Is "to go on leave" acceptable in standard English? Or is it colloquial English in my country...? :/
In my experience, "to go on leave" means to be away from work or school for an extended period of time (usually sick leave [for a long, severe illness], maternity leave, or a soldier having a few weeks off from an active duty post to travel home). I've never heard it used for just one day off. (I'm from the mid-Atlantic, US.)
It could also be used for taking annual vacation (i.e. for an extended period) but it would not normally be used for taking one day off. Having said that, it is not actually wrong. If you noticed someone was not in the office on a particular day and asked where he was, someone could easily say "he is on leave" (although the most common response would be "he's taking the day off"). However once you using "going" as in "going on leave" it would always be for a longer period. [Australia]
"I want to take time off today." seems like a reasonable substitution that's currently rejected with a suggestion for "I need to take a day off today."
I agree, "time off" or "leave" are closer to the meaning of 请假 - even if the most likely time frame is "a DAY off" 请假 is deffinatly NOT limited to meaning a single day off.
要 also means "will". "I will take a day off today" or "I will ask for a leave of absence today" should be accepted.