It's not so much that billionaires are a problem, it's that corrupt billionaires are more common than a good billionaire. I know that's the issue that I, personally, have.

Corruption is wild and will overtake anyone who has the means. Corrupt billionaire's tend to use that money to their advantage, while taking from the poor and further disadvantaging them. They'll use their money to get away with horrible crimes, or lighten their punishments, at least.