Both are physical quantities which assume a single value which is invariant under proper rotations.

So just as 3-vectors are preserved under circular rotations in three-dimensions:

The components of this vector transform between themselves as usual under rotations in space.

The components of the tensor transform between themselves as usual under rotations in space.

Further they demonstrated the fundamental symmetry of spin 1/2 particles under rotations.

The spacetime interval must stay the same under rotations, but ordinary lengths can change.

For ferromagnetic materials, the underlying laws are invariant under spatial rotations.

You now explain to them that it is better thought of as an object with certain transformation properties under rotations.

You implore them to believe that it is an object with certain transformation properties under rotations.

There are subtle differences between the behavior of spinors and vectors under coordinate rotations.