On the chance that you're not making a bad joke ...
You might as well ask "If the government is so good at medical coverage, why are there still sick people?" Or "If the government is so good at backing education, why are there still dumb people?" Or "If the government is so great at defense, why do we have to keep spending on it?"
But all right, that's the whole "the tide goes in and out" argument. Our society "accepts," for example, a minimum of five percent unemployment at pretty much any historical moment. Are you for full employment? No? So let's take this as a specific ill.
It's not like the poor are one very definite set of people, like the marielitos that Castro dumped on Florida. A lot of people are born poor who the government never get to, and if you break down how and why that is it's probably a function of budget and politics. Look, when you ask "Why are there so many poor people?" are you truly wondering "Wouldn't it be great if we could do whatever it takes to eliminate poverty?" Or are you actually saying "It's clearly a fool's errand anyway, so fuck it"?
Then there are people who find themselves poor. I guess the point here is that the government is worthless and only the private sector can truly save them. But here's the problem -- yeah, the private sector does so much of the hiring, but it also CREATES so many poor. And when the private sector drops that ball, as it does all too often -- because remember, I started the Dow watch thread -- then who will pick up the slack? Sure, a church here or a philanthropist there will help, but it's still the public sector that's left with the heavy lifting.
It's like all other problems: its only chance of getting solved definitively is if and when our whole society truly commits to that one goal. It took us nearly two centuries including a bloody war to shake off slavery and Jim Crow, for crying out loud. But since your question sounds far more about cynicism about government than concern for the poor, I'm guessing that such mobilization is still a long time coming.
The government is supposed to reflect votes, on the federal, state and local level. If you've never cast a vote with the express hope of fighting poverty, then you are very much your own answer to your own question.