Full Idea
I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication.
Gist of Idea
The various logics are abstractions made from terms like 'if...then' in English
Source
Ian Hacking (What is Logic? [1979], §15)
Book Reference
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.250
A Reaction
The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation?