It just really betrays such a selfish, entitled mindset.
What would she have said if you'd offered to provide the car and drive it as your generous contribution, but as she was needing to go there anyway, she could pay for all of the petrol and you and the other girl would tag along for free, every single time, as it wouldn't cost her any extra for you to do so?
I really don't get why being the one who owns the car - and already pays all of the considerable costs and maintenance - and can drive 'earns' you the 'privilege' of paying for all of the petrol for joint journeys as well.
Just because a joint cost isn't broken down into individual 'per person' prices, that doesn't automatically mean that everybody shouldn't pay their own share.
What next? Housemates expecting one person to pay for all the electricity for the heating and lighting, as it would cost the same if they lived alone? Would it be fair with a house with 6 (non-exempt, equally earning) adults in it for one to be expected to pay the base 75% of the council tax that a single adult occupant would incur on their own anyway, then the other 5 only pay the 5% each that it costs extra to make it up to the full 100%?
The other girl clearly understood that she was getting a good deal for a comfortable, convenient door-to-door ride and was happy to contribute for it; how odd that the CF believed that she should have exactly the same, but fully subbed by others.