Global Inequality is declining, but it is declining by the Simpson's Paradox. That is, most countries in the world is experiencing increasing inequality. The rich among poor countries becoming the global middle class, and the poor among rich countries becoming the global middle class.
This is one of the major aspect of economics that could not be unravel by the uninitiated. If people are rational to optimize for microeconomics (friends, families, and selves) then they will not optimize for macroeconomics (everyone else). Therefore, while it is good to optimize for the self, optimizing for everyone else is irrational for most individuals since they are selfless to their families, and friends, and community to a different degree at each level.