Why do Austrians say price is set by preference rather than production cost?

Because we understand basic economic theory.

Woot! Good to see my man, Mr BA himself back at it!

Econ 101:

Does OP understand that COST is short for opportunity cost: preferences unfulfilled by doing next best thing?

Demand derives from preferences and supply also from preferences, even before discussing how demand guides supply (because regardless how costly things are, if no-one wants them, their price is below cost, namely, e.g., 0).

Marginal productivity derives from price, and that is how much is then, afterwards paid for that factor of production. Mostly, then, wages and such fall if people produce what it not wanted, and cost decreases to meet price, but few people want to sell their factors of production at such low incomes. Whatever has higher price, then, get those factors.

This thread may be too long to be an effective bump, but I felt it was worth a try for this article:

What’s Cost Got to Do with It?

(Coincidentally, this is the exact same title as another Mises Daily I linked to earlier in the thread. See the “repled on” link for the other one)

Bawerk’s marginal pairs might also be useful.