In the expression 'Nothing is larger than itself', the relation 'is larger than' is

'Larger than' holds of no object with respect to itself, so it is irreflexive.

A relation is reflexive when every element bears it to itself.

Here nothing is larger than itself, so no element bears the relation to itself.

Failing reflexivity for every element is exactly irreflexivity.

The claim states this universal denial of self-relation.