How do car trade-ins work?

I don’t understand how it works. It seems like it should be cut and dried. You owe $1000 on the old car, which is worth $5000. Seems like they should take $1000 off the asking price of the new car (and still make a profit) then turn around and sell your old car for $5000. Profit, profit for them. It doesn’t work that way though.
Do trade ins benefit the customer at all, or just the car dealership?

Thanks guys