The conversation carries on. You go your separate ways. Let's say that there were actually 14 other people at the gas station at the same time you were. You only talked to one, but you didn't even give him a business card. Using a signature is like visiting a gas station and everyone winding up with your business card in you pocket without saying a word or having to approach anyone.
People have a choice to respond or ignore it.
Everyone sees your card. But no one feels like you made them take it. In the gas station scenario, you were simply minding your own business and getting gas. Your shared interest with everyone at the gas station was to get gas. Through this real world gas station experience, no one saw your business card.