Just to add to those two other points, the 360 was Microsoft's leading platform for developing countries and countries with heavy import restrictions.
For example, Brazil's incredibly protective trade policies requires electronics to be made locally if they are to be sold at an affordable price point. The 360 only went on sale there in 2011 when MS opened up a local manufacturing facility and it was the last refuge of the PS2 which only went on sale when local production began in 2009. The Brazilian market isn't large enough for MS to justify duplicate tooling and other custom production equipment needed to produce a local version of the Xbox One. However, the decline in demand for the 360 would have led to excess production capacity, allowing MS to set up a local plant with the excess equipment from underulitized original production lines.
Also, the 360-specific tooling and production equipment has long since been paid off which greatly reduces the cost per unit. The 360 provides MS with a budget offering capable of accessing developing markets which can't support the $300 pricepoint of a current gen console.
I presume the fact that Xbox one got only recently the capability to play old 360 games might have something to do with it. But which one is the cause and which one the effect?