Because of State Law. Keep in mind that the vast majority of LEOs want law abiding responsible citizens to carry. Nothing makes most LEOs happier than when Joe Citizen offs one of these scumbags (read; Antioch approx. 2 weeks ago).
Back to LEO carry,
A good example is carry in public parks. Citizens with a HCP can't carry in public parks where as a LEO can.
In fact the TCA 39-17-350 specifically states the only places LEOs can't carry: schools, without permission from principle, when drinking alcoholic beverages, where alcoholic beverages are sold (HR 218 voids that one) and when in court during precedings while off duty.
As far as private property goes, if someone were to ask me to leave / not carry, Id give my little speach and go.