firstly, depending on where you actually study, a car will be really useful for social outings, sports clubs and activity societies, and surprise surprise- foodshopping.
This is assuming your Unoversity isnt extremely urban and in the heart of a city centre. In whvih case, you dont need one. But otherwise, rural or suburban, youll probably need a car, and if not, will come in handy.
Also, if your social skills are really bad, it might help you make friends. On the flip side, people might just use you for your car, so hopefully you make friends with the right people.Sounds like your Mum is a bit emotionally manipulative of you, perhaps she herself is a bit mentally unhinged. But until you get your own place, your own job, your own life- what can you do? If youre living off your parents (like most uni students), you dont have the right to criticise them as they are still providing for you.
The key here then, is to become a negotiator and develop your diplomacy skills when dealing with family politics.
On the one hand, youre an adult, they should respect that. On the other hand, youre still relying on them, which you need to bare in mind.In short, go to uni, make some friends and take the car with you, it will come in handy. (unless youre in a city)