Technically, no... but as WD mentioned, what you really 'need' depends on the load calcs. It also depends on the physical size of your existing main panel, and if you have a space available for a breaker to feed your sub-panel. The cost is dependent on your location, as wages vary from one location to the next. Current supply chain issues have caused an increase in costs for materials as well, so don't be too surprised if it's higher than normal, or what you may have expected.
To answer your question, the NEC allows you to have sub-panels rated the same as the main. So for instance, if you had a 100A main breaker in your main panel, then installed a 100A breaker in that panel to feed your sub-panel, and had a 100A breaker as the main disconnect in your sub-panel, it's okay by Code.
Because the breakers are all in series, the Main breaker would be the one that had the most current flowing through it, and would likely trip first before your 100A feed to the sub-panel, or trip the 100A in the sub-panel. If there were some random fault in the sub-panel, then it's a race to see which breaker will trip first. (Because there is not proper breaker coordination, but that's another topic for another time.)
If I am not mistaken, you could technically feed a 200A sub-panel from a 100A Main panel... but with the understanding that the 200A breaker is not going to provide you with circuit protection and will simply be used as a disconnect. Protection of the conductors would be based on the Main breaker, or the feeder breaker.
If you have done the load calculations and know how much power your system draws, it may work out just fine.
Depending on the condition of the existing panel, its age, and availability of parts, replacing your existing Main panel might be the only option available to him. (Breakers to be used in your existing panel must be UL Listed for use in your panel. If they are not, he cannot install them per Code.) Without knowing all of the details of the project, I can't tell if the person that quoted the job is doing it right, or price gouging you. The devil is in the details, so they say.
Hope this helps.
Mark