You need to be careful taking a short exerpt like that. Nietzsche has a way of talking around the things he's talking about. I think a better snippet would be these few lines, from the 'Voluntary Beggar' in 'Thus Spake Zarathustra' (link 1):
"Then learnedst thou," interrupted Zarathustra, "how much harder it is to give properly than to take properly, and that bestowing well is an ART--the last, subtlest master-art of kindness."
...
"Wanton avidity, bilious envy, careworn revenge, populace-pride: all these struck mine eye. It is no longer true that the poor are blessed."
This gives us a little more perspective on why giving to beggars might be so annoying.
On the one hand, he acknowledges what another user has pointed out here - sometimes the poor, though worthy of sympathy because of their condition, are unworthy of sympathy because of their character. Some of them make it hard to WANT to be charitable, owing to their obvious feelings of spite and hatred. How many of us have been cursed by a beggar for NOT giving to them?
Contrariwise, even if you could find a 'perfect' poor person, giving itself is not so simple an act as it seems. How many people have lived their lives contentedly only to be ruined upon winning the lottery? So too is it not uncommon for a person to want something other than what he truly needs, as the beggar who took money but not food or a job. Sometimes the perfect charity is refraining from charity.
If all this is the case, then one might wonder if the world would not perhaps be a better place with no beggars whatsoever. Let people learn and practice the 'art of giving' when there is not so much to be gained or lost, and let those who would recieve charity do so humbly and quietly instead of with demands. I'm not going to go quite as far out on a limb as Nietzsche on this one, but I have to grant that he has a point.