It's probably not _specific_ to Euclidean geometry, but in the american school system it's common to see proof-based geometry in high school, while you generally don't dwell much on the proofs of calculus unless you take a real analysis class at university. So it's more about timing/exposure than the field itself.
The US high school math curriculum relegates deductive proofs to a course in “geometry”, which typically ends up being a somewhat watered down version of Euclid, with a few extra topics tossed in at the end.
Arguably there are better subjects to use for teaching deductive reasoning, and better formalizations for teaching geometry. This particular approach has a lot of historical inertia though.
If you pick up a modern calculus book, one advantage over Euclid is that the proofs will actually be correct ;)