Why did Gottlob Frege prefer an intensional logic of concepts?

Gottlob Frege’s preference for an intensional logic of concepts—as opposed to an extensional logic of classes or sets—was rooted in his foundational approach to mathematics and logic.

Frege held that mathematics could be derived from pure logical laws, a position known as logicism. Central to his work was the belief that logical analysis should focus on the "thought" expressed by a sentence rather than merely the extension (the collection of objects) to which a term refers. He maintained a strong hostility toward British extensional logic and the empiricist tendencies of thinkers like J.S. Mill, viewing them as inadequate for the rigorous formalization of mathematical reasoning.12

Furthermore, Frege’s distinction between sense (Sinn) and referent (Bedeutung) allowed him to account for the informativeness of identity statements, such as "Venus is the morning star." By focusing on the "mode of presentation" (sense) of an object rather than just the object itself (referent), he developed a conceptual framework that prioritized the logical structure of thoughts over the mere grouping of extensions.34