I'd recommend something like

We want something that corresponds to the intuitive idea of order. Let's unpack this intuition. <motivate reflexivity, antisymmetry, transitivity; discuss.> Now, given that some relation R has those properties we are then justified in using the symbol ≤.

In other words, you don't need to hide your destination -- you just need to make it clear that intuitive labels are a privilege entitled to objects that have demonstrated good behavior.