If you want a more complex answer:
Microsoft as a whole makes far higher profit margins than gaming industry, Xbox existence came down to Ed Fries et others convincing Bill Gates that Sony was taking over the PC Gaming space and therefore, the PC space itself, which was a major threat to Windows, and PC gaming suffered in the 00s with plenty of studios dropping their commitment to it and go for Playstation, Xbox and Nintendo instead.
Fast forward, PC gaming is in full force, Sony is porting their games to the platform, the budget costs are so huge that developers make multiplatform as a priority since porting is a dot in the budget sheet, Microsoft probably see this as evidences that they will never be threatened in their core business and Xbox can exist as a profitable per unit niche than a slim margin popular brand (think like automakers, they have been killing cheap cars for SUVs for this reason).