Actually, you're right, but not for the reason you think. If everyone gave money to beggars every-time they saw one, pretty soon we would have nothing but beggars.
On the flip side, "If NO ONE gives to beggars there won't be any beggars!" is also correct, but not for the reason given. Reality is that most beggars would die relatively quickly because they're not there by choice or because they think that begging to live is better than finding a job. Yes, a few are there by choice for one reason or another, but I really hate the world where people choose to let the honest ones dies to spite the few freeloaders.
I think if we were to start over as a society without the social norms of begging like we have now and everyone were to give if they saw the 1st person ever on the street things might be a different and we might not have people who are on the street for extended periods like we do now.
I wonder if there's a way to test this out.