I would like to understand a context. I asked someone a question "how is life going for you besides writing ?" what I meant by this question is ( I am not an English native speaker ) I want to know about the person, show concern and care. That´s how I show care and concern asking this question in my culture.

so I asked : How is life going for you besides writing ?

and the answer was: passably well. Classes are fine, but growing increasingly tired of Lenoir.How about you?

I interpreted the answer as the person answring me only about work, as if the person didn´t want to get into his personal life, as if saying , that´s not your business.

can someone help me with this? Was the second sentence giving more details about what was said in the first and it was just talking about work?

or the first sentence is different from the second one. I mean, first sentence talking about his life in general and the second one as if saying besides that classes are fine and growin ...

In English, asking how someone is doing is just a conversation starter.  It does not require much of an answer, if any.

"Good morning, how are you"

Fine, and you?


So by asking the question you asked, you are not getting the information you wanted because the question is not asking what you intend.  The person's response is normal and is not telling you to mind your own business.

I do not know the culture you are in nor the culture of the person you are interested in learning more about so it is difficult to advise.  One possibly is to simply ask "Tell me about yourself".  Or "I don't want to be rude, but I was wondering if you would tell me more about yourself.  I would really love to know more about you".
I should mention that if you do not know the person reasonably well, they may not want to discuss their personal life.  Many people are very "private"