Used cars are a thing. Albeit not identical, dealerships definitely do sell other vehicles and will almost always push the new model of their brand over the used model of the other brand.
I'd argue this will vary with dealerships. And, the pushiness would be more sales person, rather than the dealership.
For new cars, there are a couple reasons why a dealership may push a new car over a used car. The manufacturer may be providing volume incentives and the dealership needs to sale a certain number of models to meet that incentive. Or, a new vehicle has been sitting on the lot for too long and the dealership needs to move the vehicle (this is more true for used cars).
But, USED cars are a cash cow for dealerships. Either through trade-ins or auction purchases (based on the type of dealership), there's WAY more margin in a used vehicle than there is in a new car.
Unless it's a purely volume-driven dealership, dealerships will be perfectly happy to push a used car over a new car.