user123, Ryanair’s own terms and conditions say your girlfriend can travel on her ID card:
https://www.ryanair.com/gb/en/useful-info/help-centre/ryanair-uk-terms-and-conditions0
“2.1.2 A valid national identity card issued by the government of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Estonia, Finland, France, Germany, Gibraltar, Greece, Hungary, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Netherlands, Malta, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden or Switzerland”
There is verbiage that (correctly) says she cannot travel TO the UK on an identity card, but there is nothing to say she cannot travel FROM the UK.
“From 1^st^ October 2021, nationals of the EEA/EU or Switzerland travelling to the United Kingdom must be in possession of a valid passport, as National ID cards issued by the EEA/EU and Switzerland are no longer acceptable to enter the UK (unless you hold a form of residence status in the UK)”
I’m sceptical about the response you received, which doesn’t sound like it came from a native English speaker. I do not see how Ryanair could possibly deny a passenger with an Italian ID card from boarding a flight to Italy without falling afoul of EU-261 rules.
If all else fails, try Easyjet or British Airways. I’ve travelled with both on an old-style Italian carta d’identita’ within the past three months, so I know first-hand it’s possible.