Living in a bad neighborhood exposes you to an in-ideal living atmosphere. The people you are around influence you in many ways and one of those ways is the wrong way --not because people in the neighborhood want bad things for their brethren --but because their way of life and expectations impinge on the growth of the new young people in the neighborhood with respect to the wider society.
Also, it's worth noting that widening inequality is a global phenomenon but not only between people but amongst nations. The inequality between let's say Mexico and Finland was different back in 1910 and what it is now. The inequality between poor and rich in the US was also less in the US back in the early 1900s.