On the other side, the usual problem of poor is money, food on the table and job. Rich people are the ones who can provide job for the poor, so by helping the rich, you also help the poor, though not directly.
I agree with you and some of the comments here, we just need to solve the problem of the rich, then the problem of the poor will automatically be solved. The rich and the poor are interdependent, and neither would survive without supporting each other and our society would cease to exist. The role of both is very important, but the people who control this world are the rich, so if we want to solve the problem, we need to solve the problem of the rich.