Poor is poor is poor.
Nor really. There's poor as in "I can only afford a second-hand Fiesta when my neigbours have BMWs", and poor as in "my children are cold and starving". There's even Dickensian poor, where the workhouse was the only option. We can never realistically hope to remove everyone from the first category, working to fix the others is of course important.
A country as rich as ours shouldn't have poor
It will always have poor, simply because we can't all be equal.
or at least should have something in place to give those in that situation the best chance to get out of that situation.
No argument there, and a good education system is paramount. You can't always make people take advantage of it, though.