The airlines and the online travel booking engines all have disclaimers saying that it is the travelers responsibility to have all appropriate documents and they have no liability for a passenger failing to do their due diligence.

The 3 month rule is available on the website for the Embassy of Italy.

Those are the rules and the airline has to follow them.

It would have been worse if you had been denied entry into Italy and sent back. At least the trip can be salvaged with less cost.

I did an expedited passport in 2014 as I would not have been able to enter into Germany for the same reason.

As people book book up to a year in advance and visa issues can change there is no way to run the passport number and expiration date against a worldwide database with all the regulations and keep checking for changes. That is the responsibility of the traveler.