tired can mean تعبان, مريض, ليس بصحة جيدة لماذا تترجمون الكلمة بمعني واحد فقط؟؟
No. Tired cannot mean sick or unhealthy. That's incorrect. One can be tired because he is sick or unhealthy, but being tired or sick/unhealthy are two different things.
Yet the word ta3baan is used in the Middle East in spoken language as a synonym for sick. A Syrian would rather say he is ta3baan than using ma3riD as a Moroccan would do.
Yeah, but isn't that more of a euphemism? Germans also often say they are tired (müde) when they are actually sleepy (schläfrig), but that doesn't change the meaning of each word. The standard meaning of تعبان is still "tired", which is very different from "sick", and it wouldn't make sense for the course makers to confuse learners with a dialect usage of it.