I think calling a doctor big is not very nice....how about My son is a great doctor. :)
this is because they are using a dialectical expression instead of a correct Arabic one
My son is a large doctor was not accepted, but large is given as a meaning of the the third word.
The whole expression is wrong in fact. They are putting dialect (again) into use here instead of proper Arabic. They should have used "famous" instead of "big" (Arabic: مشهور Mašhúr).
Big and little can also be used for age (think big/little brother or sister). Maybe a better translation would be his older son is a doctor?
I think they are basing this sentence on dialectical Arabic. Specifically Egyptian, where using the adjective "big" means "famous" or has a name in society. I don't think they are talking about age here. Anyway, knowing Duolingo for 2 years now, I wouldn't be surprised for such weird sentences after all.