I mean to say that anybody can hatch a chicken's egg under a toad, (even Neville can do that with his own toad ), so why are they so rare that there is only one in all of Hogwarts?
Fantastic Beasts and Where to Find Them suggests an answer to this:
[S]ince Basilisks are uncontrollable except by Parselmouths, they are as dangerous to most Dark wizards as to anybody else, and there have been no recorded sightings of Basilisks in Britain for at least four hundred years.
Fantastic Beasts and Where to Find Them "Basilisk"
To put this another way: a basilisk is a serpent that only responds to an essentially-dead language1 and kills (or, at best, petrifies) with the slightest glance.
Sure you could breed one, but why would you want to?
1 I think in the entire Harry Potter universe there are only a handful of confirmed Parselmouths: Salazar Slytherin, Herpo the Foul, the Gaunt clan, Voldemort, and Harry (temporarily).