Unless it has a lot of detail stained or clear-finished detail or gingerbreading or such, which yours does not sound like, I can't see more than roughly half that for a "normal" repaint job. But yours is not a normal repaint - if peeling significantly then stripping to bare wood and sanding and priming/painting is a LOT more work - more than double. Your job sounds like it is including a pretty fair amount of scraping and sanding to prep the surface, probably double-prime (penetrating primer plus paint prep primer) and two-three color coats paint.
But - if you were getting funny vibes from the estimator and neighbors have had similar jobs with bids for about half that, clearly both because you are iffy and because it is a larger $ value job, sounds like you need to find some more well-rated and reviewed painters in the Home > Painting - Exterior category of Search the List to get some competing quotes to see just what is "reasonable" for your particular house.
Typically around $1-3/SF (of painted area) commonly (on up to commonly $4-6 with pretty heavy scraping/blasting/sanding). In your case, 2 story so about 1100SF per story, say 25x45 footprint = about 1400SF per story assuming older house with 10' stories = 2800SF, so with a lot of prep commonly $11,000-17,000 complete, ballpark.
The other possible factor - if this paint contains asbestos or is lead painted (original or very old paints), then all of a sudden you go from the above to lead paint abatement and repaint job (which is likely if multiple peeling layers) then around $7-15/SF is more common to remove and then prep and paint - so more like $20,000-40,000 range !
So - depending on whether bid includes lead paint work, and you need a clear-cut determination of that and by a lab the contractor/bidders accept, BEFORE signing a contract so they don't bid a no-lead job and then say - OH, that doubles or triples the price because it has lead paint. Given the age of the house it is highly likely - indeed almsot certain - unless you have a prior certificate of abatement for the entire exterior. That might have been part of the vibes issue - could be he was not quoting lead but was thinking it was almost certain.
Certainly if lead paint abatement is necessary then bid sounds on the low side - otherwise on the high side, but might be legit if he was thinking total removal to bare wood, penetrating wood preserving primer, possibly a bit of rot repair, then "base" primer and 2-3 coats color coat of paint - the other bids on neighbors, if similar size houses, might have only been for light scraping or pressure washing for the loosest paint, then only touch-sanding but not removing that paint still partly sticking, and only one primer coat or maybe none, and maybe only one color coat. And of course, the paint quality itself can make as much as about $0.50/SF per coat difference between cheapest and highest quality paints.
You can find a fair number of previous similar questions with answers and ballpark cost info about house painting (both interior and exterior), in the Home > Painting link, under Browse Projects, at lower left.
