I like wine, but I am drinking milk. — J'aime le vin, mais je bois du lait.
Is it correct to say "J'aime du vin, mais je bois du lait", because "le vin" sounds more specific to "this wine" rather than wine in general?
"J'aime du vin" is not right.
You can say :
J'aime BOIRE du vin / J'aime Boire du lait / J'aime BOIRE de l'eau
j'aime le vin / j'aime le lait de brebis / j'aime l'eau gazeuse...
But you can say :
Je bois du vin / je bois du lait / je bois de l'eau
After the verb aimer or adorer you use only the article instead of de + the article. So j'aime le vin instead of j'aime du vin.
All other verbs that I can think of right now you use de + the article, je bois du vin, j'achete du vin etc.
If you say "je bois du vin", that means I'm drinking wine. Or, I'm drinking some wine, but you don't need to say "some" in English. If you say "je bois le vin", it means you're drinking THE wine, or all of the wine. In this case we know what wine we're talking about, as opposed to all the wine in the world.
So you say "j'aime le vin", which means you like wine in general, but you are drinking some milk, "du lait", not "le lait" which would mean you're drinking all the milk. If you have a roommate the opens the fridge and there is no more milk, it's all gone, he/she would say "est-ce que tu a bu le lait"? We know what milk we're talking about. It's finite. But if you say "j'ai bu du lait", it means I drank some milk.
J'aime le vin, mais je bois du lait >> I like wine (in general, all wine), but I am drinking milk (some, not all the milk in the world). "Le" means "the" sometimes, but also it generalizes your remark. I agree with Seattle_scott.
Check the "Tips & Notes" for the Food lesson. This rule is explained very well there. Basically, one of the times that you MUST use the definite article in French (le/la/les) is before the direct object (in this sentence, "vin") of a verb of appreciation (in this sentence, "aimer"). Hope that helps.