I prefer living in town than in countryside.
Hello!
How would you explain to a student that this sentence is wrong?
"I prefer living in town than in countryside."
I would say it "I prefer living in [a] town [rather] than in [the] countryside."
Is my correction correct?

Question

Answer

The first sentence could be correct but replacing 'than' with 'to': "I prefer living in a town to living in the countryside." This is because prefer has different constructions from the comparatives.

Your option is also correct. Prefer... to... Or Prefer ... rather than (instead of) ...

Answer

Your sentence is correct.

The other sentence is correct with a small change ('the countryside, not 'countryside')
"I prefer living in town than in the countryside". 
Saying ('town' instead of 'a town') is more often said when you are referring to the town that you are currently living in, though it can be said in other circumstances as well.

Answer

I prefer to live in town than in the country(side).