The host is responsible for creating and maintaining the listing. AirBnb do not have any input into the listing.
‘Breakfast is provided’ is listed under ‘Special Amenities’ - ticking the box means the host provides breakfast as part of the cost. If the host wants to charge for it as an added extra, they need to indicate this on their listing with prices and then they can charge for it through the AirBnb Resolution Centre (in accordance with AirBnb policy that guests should always pay hosts through AirBnb, not directly to the host).
I would expect the host to state what type of breakfast (basic, full cooked etc) is provided within the listing description. If there is no mention of an extra fee for breakfast anywhere within the property listing, you should contact AirBnb Support to resolve the issue.
Source: I am an AirBnb host.