Why? Because in the used car supply chain, the trade-in is the start of the chain - the lowest possible price, and the worse possible deal.
The supply chain (in its longest form) looks like this: Used car retailer sells a car (end of chain). He buys the car from a wholesaler. Wholesaler buys a car from an auction. Auction gets its supplies from dealerships. And what cars are dealerships putting in the auctions? Trade-ins.
Now, that chain can be broken at any time -- that's just the longest version. But dealers calculate trade-in prices with the assumption of a worst-case scenario (that they won't be able to sell on the lot and that they'll have to dump it to an auction).
So moral of the story - if you have the time and know-how to sell direct, do it!