"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.
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.