I don't think "hanem" is correct here, since bugs are also insects. The English sentence means "No, ants are not bugs either, but they are insects anyway."
If I'm not mistaken, "de" would be correct here instead of "hanem" then?
Yes, that's exactly what I meant.
I see it as they were talking about (say) flies. And one person says "Flies are not bugs - unlike ants" and the other person says "No, ants are not bugs either, but they are insects".
Ez a mondat nem logikus sem angolul, sem magyarul.
the is not in the sentence where did "a" come from