Galeano means that charity is the hegemonious class (top) giving to the proletarian classes (bottom), thus vertical (up-down), and that solidarity is is unity and care within one class, thus neither going up nor down, but rather left and right.
Why Galeano doesn't like charity from the top to the bottom is obvious - because it is humiliating, because it doesn't address the real issues, because it isn't genuine (often PR coups, see Trump offering to donate $5 million to any charity in return for Barack Obamas school records), etc.
I'm not a fan of Occupy, I knew it would capsize the second it emerged because it was filled with class collaboration and liberal concepts and ideas, but "rationalhub" is correct when s/he says that there is a big difference between "charity is bad" and "I dont believe in charity".
Charity isn't necessarily bad, but it shouldn't *have* to exist. It is a result of the material realities and conditions of the world we live in. And it does not address these issues, it is merely a pretty poor bandaid on a problem springing from the roots of all hierarchial and class systems.