"I cook dinner at home, even though my brother eats it."
Translation:Дома я готовлю ужин, хотя ест его брат.
There is nothing grammatically wrong with your sentence, but the one offered by DL certainly sounds better. It makes the "even though" part work better by opposing "я" and "брат". You are using the most standard word order in both clauses, which does not stress any particular words in an obvious way. The offered translation rearranges both of them in order to stress "я" and "брат".