First, your car is legally registered in your name. Most curbstoners don’t bother to register the cars they sell. Instead, they quickly flip their vehicle purchases so the title transfers from the previous owner to the new owner, skipping the curbstoner.
Second, you probably have only one or two cars to sell. A typical curbstoner, being an unlicensed dealer, sells several used cars a month, every month, all year long.
Curbstoners pretend to be private parties, but they’re not. They’re unlicensed businesses, making a profit with no accountability, regulation, or recourse for their customers.