Who said anything about disagreements, much less outrage, though? The context was cutting out noise, and muting is a more effective version of skipping your eyes past it. Some topics just get spent and become boring.
The article was basically about this ("So I began to take note each time I experienced a little hit of outrage or condescension or envy during a Twitter session. What I found was that nearly every time I felt one of these negative emotions, it was triggered by a retweet."), and in my experience this is largely how the "mute" functionality is used: literally to protect yourself from experiencing the learned emotional trigger associated with seeing specific keywords or phrases.
Fair enough, but this subthread had diverged to a discussion of the logistics of reading a large number of feeds, and the mute functionality was suggested in that context.