Austenitic stainless steel is non-magnetic because of its crystallographic structure. In an austenitic lattice the atoms are arranged so that orbiting electrons cannot align their spin in a consistent direction, and without that alignment the metal cannot become ferromagnetic.
Which stainless steels are magnetic?
Iron, nickel and cobalt are all magnetic - or, formally, ferromagnetic. Stainless steels are all magnetic except those based on a purely austenitic microstructure, so ferritic, martensitic and duplex/super duplex grades are magnetic.
Why the austenitic structure behaves differently
An austenitic microstructure refers to the lattice that the atoms align to in the solid state. The significant nickel additions in this family of stainless steels force the microstructure to exist as austenitic rather than ferritic.
Ferromagnetism - the ability to be attracted to a permanent magnet - is associated with the electrons that orbit the nucleus of an iron atom. In other microstructures the spin of these orbiting electrons can be aligned by an external magnetic field, and the metal appears magnetic. In an austenitic structure the arrangement is more random at the atomic level, so the electrons cannot align their rotation consistently, and the metal appears non-magnetic.