As a 50 year old married to another 50 year old, I moved to the back seat when my MIL got in the car.
Did she expect you to do that, though? Was she fit and well for her age or did she struggle with mobility in the way that a lot of people approaching/over 80 naturally do?
It might be ageist of me, but I would probably do the same for an elderly person, as they do often struggle more to get in the back; but if I were a young adult and it was a healthy middle-aged adult joining the journey later, I don't know if I'd automatically think to move.
Also, if the two parents have been divorced/separated for a long time and the adult child is very used to being alone in the car with his/her Dad, it may never actually cross their mind. Whether it should is a different question, of course.
Moreover, you'd think they'd be more mature about it at 22, but if they see you as competing with them for their Dad's affections and attention - and that you're 'replacing' them (they should realise at 22 that their parents want adult relationships as well as parent-child ones, I know), that might come into play too.