So your problem with the meme isn't it's equal application of logic, it's with a perceived false narrative the meme has, which suggests that pro-2A types think anti-2A types want to ban guns? Sigh... I don't know why you couldn't have just said that in the first place, if you actually felt that way.
I think you've hit the nail on the head in terms of why us pro-2A folks don't want *any* *more* gun control laws; it's because we think it will lead to banning all guns (which is unconstitutional, btw.) And I think if anyone who is in favor of *more* gun control laws was being honest with themself, they would have to agree that that's exactly what those in the anti-2A movement want, or at least what the movement's leaders want.
I agree that while the meme makes guns and cars seem similar, there are some obvious, and significant dis-similarities. Rightly or wrongly, cars are viewed as necessary tools for the individual to use in making a living, which in almost all cases is not true for a gun. I think people probably feel that convicted felons who have served their time, are trying to live a law abiding life, don't need being banned from driving added to the list of hurdles for them to overcome in order to live that law abiding life. otoh, the right to keep and drive cars is not specified as the second amendment (and they made it 2nd, after free speech, for a reason.)