@Sahil11
There are three types of invitation letters acceptable to make an application for a Russian visa.
Tourist - Work - Private.
Tourist invitation letters are issued only from Russian officially registered travel agents or by large hotels chains who have there own registered agents office - This type of visa 'tourist visa' is the likely choice for most visitors, including airbnb using visitors.
Work invitation letters are made in conjuction with employers and the Russian Federal Migration Service.
Private invitation letters can be requested by individuals resident in Russia (like your host), but these are very time consuming to obtain and really these are best suited only for homestay friends or family who are visiting for a longer period of time.
In respect of this, your host is not refusing to issue an invitation letter, it just means they can't automatically do this.
You still need an invitation letter as one of the documents required to apply for a visa though. Your application will be rejected without one.
To get a tourist visa invitation letter, it's quite easy on-line to order one (I can give you further info by private message if needed.)
However, look out, there can be a big variation on prices charged by different agencies.
A host can go to a local agent to get an invitation made. Be aware though they will have to pay upfront to the agent ( from around 20 dollars per letter) and it takes time to go plus they need to obtain some personal details from you so overall there is a reluctance for most hosts to do this.
You should note too, on rare occasions some Russian consulates ask for the original invitation letter rather than an email copy (for example Latvia) - worth also to check first.
As far as booking a hotel on booking-com - I'm sure that they do not support sending out invitation letters automatically. Like I said, big chains (for example Park Inn) have the facility to issue invitation letters directly - however if you cancel your booking with them they usually attempt to reclaim at least the cost of the invitation from your credit/debit card as compensation.