Officially, Google killed Reader because "over the years usage has declined". I believe that statement, especially if API clients weren't considered "usage", but I don't believe that's the entire reason.
The most common assumption I've seen others cite is that "Google couldn't figure out how to monetize Reader," or other variants about direct profitability. I don't believe this, either. Google Reader's operational costs likely paled in comparison to many of their other projects that don't bring in major revenue, and I've heard from multiple sources that it effectively had a staff of zero for years. It was just running, quietly serving a vital role for a lot of people.
Google Reader is just the latest casualty of the war that Facebook started, seemingly accidentally: the battle to own everything. While Google did technically "own" Reader and could make some use of the huge amount of news and attention data flowing through it, it conflicted with their far more important Google+ strategy: they need everyone reading and sharing everything through Google+ so they can compete with Facebook for ad-targeting data, ad dollars, growth, and relevance.
RSS represents the antithesis of this new world: it's completely open, decentralized, and owned by nobody, just like the web itself. It allows anyone, large or small, to build something new and disrupt anyone else they'd like because nobody has to fly six salespeople out first to work out a partnership with anyone else's salespeople.
That world formed the web's foundations -- without that world to build on, Google, Facebook, and Twitter couldn't exist. But they've now grown so large that everything from that web-native world is now a threat to them, and they want to shut it down. "Sunset" it. "Clean it up." "Retire" it. Get it out of the way so they can get even bigger and build even bigger proprietary barriers to anyone trying to claim their territory.
Well, fuck them, and fuck that.
Current Music: Add N to (X) -- Buckminster Fuller ♬