The leadership was never completely honest about why Reader was shutdown, and the stated reasons didn't pass some basic sniff checks. But it was easy to read between the lines: the executives' attention was on other things, and Reader was a threat to their growth. But also it was a passion project that a company like Google would struggle to keep updating since it brought in little revenue (even though there were hordes of people volunteering to maintain it for free in their 20% time).
The decline of RSS among a certain audience was only peripherally related to the elimination of Reader; it's not like there aren't other RSS readers out there even if Google makes a convenient villain. But Google did whiff on social in general and certainly indexing the world's information became a very secondary goal especially after failing with some efforts on the copyright front.