The chat he had with his sister about "car stuff" that you didn't understand probably isn't because you're not a driver, it's because you're not a "car girl" and not a mechanic. I drive and "car stuff" could still be things I don't understand. I think you're just feeling badly about yourself and projecting a bit there.
Cars aren't typically called "his" or "hers" based on who owns them, it's not something you can know from a glance, it's based on who's driving it. So even if the car is in your name, it can be yours, or his, or the family car. You don't drive, so it makes sense the people just assume it's "his". It's not meant as a slight, you're just feeling sensitive about it. We have several cars, all but one in my DH's name, the one's I drive are "mine" and the others are "his" (even though yes, they're "ours" we don't refer to them in that way). He's also calling it "his" because he's the one driving it, and the only one able to make use of it. Probably also a little because it was "his" car that was traded.
Also, your last post If the car was in dhs name and he was paying then it would be his car.though id like to think that we are a team and its ours. Which is not how you feel about "your" car.
I don't think this about the car, this is about how you feel dependent on him, how you don't feel like he respects you, and how you'd like to do stuff without him because he's not very gracious about it.
FWIW you probably won't be very good at first... learners rarely are, that's why you're learning. You probably also may get into an accident, you also may not. It also doesn't need to be because you're a bad driver, but could be because your reactions aren't the same as someone who's been driving for years. It really is a "years and years of practice" thing that has you reacting in a certain way. It's also nerves, where a long time driver is more confident in their ability. Not to mention some people really suck at driving (over confident, dangerous, bad) and you will be on the road with them.
Also, the size of the car DOES matter. I have a mid-size. I don't like smaller cars, and the bigger cars are a bitch to maneuver and park. I also don't like station wagons (or other vehicles with the rear window so far back). I drove a "sports car" and it's too low to the ground, I don't like it. I drive another one that's pretty popular and I didn't like the way the head rests blocked my blind spot. My SIL just got a new car and she's short so the mirrors obscure her view of the front tyres.
Perhaps if this car is the wrong size then you should trade it in for a more friendly vehicle for you to drive and learn in, or perhaps even 2 smaller cars. I do think you're taking this far more personally that he intended it to sound.