Full Idea
Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics.
Gist of Idea
Classical logic is deliberately extensional, in order to model mathematics
Source
Melvin Fitting (Intensional Logic [2007], §1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2