"I am here without a family" is bad English and would hardly ever be used by a native English speaker. "I am here without family" is much more common, but Duolingo rejected it. This should be changed.
There are multiple reports on this, and as a native AmE speaker, I agree with you. "I am here without family" is now an accepted translation.
So, I guess "rodiny" is the genitive form of "rodina", isn't it? Since other slavic languages use genitive after "bez".
I put "I am here without the family" as this is quite a normal thing to say in English when one means "my family" and I think that should be accepted too, especially as there is no specific reference to "my" in the exercise.
You must use the report button. The sentence you propose is accepted. Future comments like this will be removed without any response.
OK, but then others do not see the reasoning behind acceptance or otherwise of the finer points of acceptable translations.