"The new airports are not small, but big."
Translation:Az új repülőterek nem kicsik, hanem nagyok.
Why does "uj" not pluralize into "ujak" like kicsi (kicsik) and nagy (nagyok)?
Új is right before its noun, modifying it as an adjective. In that case an adjective doesn't pluralize or take other endings.
kicsik and nagyok are actually the predicates of the sentence. They rename the subject, and in English, they come after the appropriate form of the verb "to be". In that position they take endings to match the subject. Note that they basically behave as nouns in this position: the setnence could be read as, "The new airports are not small ones, but big ones."