It's inevitable that poverty will end, we'll always have the poor in our world and we can't help them all
So it's
not inevitable that poverty is going to end--and if that's what you're saying, I have to agree with you. Poverty, homelessness, drug addiction, all of these problems are going to be around as long as humanity is. Think about how long humanity has been around and how much progress has been made in so many areas, and yet we've still got enormous wealth disparity all over the globe and there isn't a government or private organization that exists or has existed that's been able to rectify said disparity (or the other problems I mentioned).
This is why I have a grudging respect for some of the billionaires who donate a good portion of their wealth to charity. Warren Buffett isn't leaving all of his wealth to his children, for example (which I find kind of funny). I forget who he's bequeathed it to, but he's made it clear that when he dies his money is going to be put to good use.