It's pretty much industry standard that the name in the PNR/ticket should match that on the passport. What you are normally known as is irrelevant.
My great Uncle was known by his middle name all his life but wouldn't put that as his first name on the ticket on one of his monthly trips to either the USA or Spain. The name simply wouldn't have matched his passport, which is what the airline specifically ask for. There are plenty of reasons why they want your first name on the ticket, so you should, rightly, be charged to change it if the airline demand that you do.
This begs the question why is the first name ok and not the middle name
If it is a question of the name on the ticket matching the name on the passport, then either a match on the surname and one of two (or more) given names is enough, or it is not. There is no justification why the match should be on the given name that happens to be listed first in the passport. For someone named John David Smith, "David Smith" is exactly as much a match to the passport name as "John Smith" is. I don't believe there is any kind of legal distinction between "first" and "second" or "middle" names in most Western countries: there are just surnames/family names and given names. (The European and Australian passports I have seen are certainly like this - maybe US is different?)
An airline might be within its rights to demand an
exact match to the passport name, in which case the ticket would have to be in the name of "John David Smith". But if they allow "John Smith", they have no basis to disallow "David Smith".