But the economical and social situations are different in rich countries. In a poor country many people are poor, usually because there is something keeping them poor, be it war, famine, government oppression, societal oppression, or something else. In such a country this argument works: you have to make begging so economically unattractive that few people would do it because they could make more with less effort by overcoming whatever problems are making them poor. Not to mention that if too many people become beggars the begging industry might collapse because there would be too few people producing things for the beggars to buy.

In a rich country, there is a strong social stigma attached to begging. Some cultures make exceptions for beggars with particular obvious reasons for begging (injured war veterans, orphans, etc.), but to my knowledge no rich society considers it acceptable for a person who could earn a living by other means to beg. And, being humans and not "economic men", the people in those societies feel that pressure and will go to extreme measures to avoid begging, including resorting to theft (albeit a career choice made possible by having a large population with enough money to have things worth stealing). So in a rich society it probably actually doesn't hurt to give money to beggars, and may even help because it might make begging attractive enough to overcome the social stigma that pushes some people to commit crimes.

That's my armchair social analysis. It feels like it's at least a shadow of reality, though, if not more.