They don't show the reserve price because having a secret reserve is supposed to (and I guess they are correct) get the highest price for the seller: it is supposed to encourage bidding, which results in interest and excitement for the auction, which encourages others to bid more than they ordinarily would have.

Suppose you had something worth $100, and you start the auction with no reserve and an opening bid of $80.
A lot of potential bidders might scoff at that, think there is no bargain and feel peculiar about starting off so high (a lonely, exposed, foolish feeling). So no one ends up bidding, let's say.

On the other hand, let's say the same article is given a $10 opening bid and an $80 reserve. It is supposed to attract a lot of low bids from bidders who (a) like to see their name in print on the bidding sheet, and/or (b) are hoping for a miracle (ending up winning it real cheap). This encourages others (gives courage) to bid -- they feel it has value (witness the other bids) and they are not alone anymore.

I never liked reserves, but I wrote enough already.