CO2 emissions, health and education

"With Earth's human population reaching 7 billion in the past month" it is Time to stop celebrating the polluters (in Nature). Chuluun Togtokh wants the Human Development Index (HDI) of the UN to incorporate CO2 emissions because he thinks both that CO2 emissions are a proxy for unsustainability and that the HDI as currently constructed "encourages countries" to behave irresponsibly. CO2 emissions are not a good measure of unsustainability, "countries" don't behave, and I doubt anyone tries to earn more, educate himself or live longer just to increase the HDI of his country. But I want to focus on another bizarre statement:

Emissions are positively and strongly correlated with income; less so with the HDI; and not at all with health and education.

Togtokh doesn't say how he got these results. But they look wrong. According to Gapminder World, CO2 emissions do correlate strongly with income:

And more or less equally so with the HDI:

And also with life expectancy (the measure of health in the HDI):

With child mortality (not included in the HDI):

And with years of schooling, the measure of education used in the HDI (the graph includes the data for women, but an even stronger pattern applies to men):