Why does Chinese lack some level of abstraction in some idioms? (e.g. 兄弟姐妹) Example: in Chinese, you can't* speak of siblings in a general term, and in turn you have to enumerate all 4 combinations of sex and age: 兄弟姐妹 ( older brother, younger brother, older sister, younger sister )   

Can you name other examples like this, and do anyone have any clues or explanations about why is this?  

I think it might be in part due to Chinese being a very old language and carrying some aspects of more primitive ways of speech from long ago, but it's just speculation.  

* as far as I know
Your question is a bit hard to answer because you can't say a word doesn't exist just because it's a combination of several related characters. This is how most words are made in Chinese. It would be like saying that you can't speak of psychology in a general term in English because you have to describe what it is every time (psychology = psyche + logia (study)).

Basically, 兄弟姐妹 is not really an enumeration, it's a word, just like 同学 is not a description but also a word. How these words are composed is mostly incidental (although it's often relatively logical and consistent).

To go back to your question, other examples of "enumeration-based" words I can think of are 夫妇 (couple), 父母 (parents)