What type of vehicle do I need to tow a 5th wheel with a GVWR of 9650 lbs?

I would like a less powerful/cheaper truck that gets better gas mileage. If a Ford F150 can tow 12,000 lbs, why would this not be adequate? According to the online salesperson, I need a F250 or F350. They say a F150 can't tow a 5th wheel.

Added (1). So, I could tow a travel trailer weighing 9650lbs, but not a 5th wheel weighing 9650lbs?

It doesn't have the same wheel base or engine, and you have to consider some contents. I have insured hundreds of people with 5th wheels, not one of them uses a F150 to do so. Some have attempted it, but it blew their transmission, brakes or a list other of issues. If you want to pull something with an F150, consider a pop-up camper. Otherwise you will need a bigger vehicle for a fifth wheel.

The suspension and chassis is simply not designed for that weight attached to a 5th wheel coupling.

A trailer for a bumper level hitch is balanced very differently, with maybe only 10% of the load placed on the tow vehicle. So your F150 can handle 1200 lb down load on the hitch, and the rest is on the trailer axles.

But when you go to a 5th wheel load, much more weight goes on the hitch. Because of the way the trailer is balanced. If it's not built to handle this it will damage the vehicle. Fit the wrong hitch, overload your vehicle and bend the body, GM are going to tell you to go away, and it won't be covered by insurance either.