First of all, I'm a big fan of both your companies, Twitter and Square, and I've always admired what you've had to say in the press about the philosophies and principles underlying those products. That's why I was disappointed to read that you were renouncing the word "user" in favor of "customer" at Square.
You started your post with a dictionary definition of the word "user". I'd like to start by turning your attention to its root:
[verb] take, hold, or deploy (something) as a means of accomplishing a purpose or achieving a result
You describe "user" as a "passive and abstract word". But there is nothing passive and abstract about the notion of use. It's about as active and concrete as a concept can get. Look at the words in that definition—solid, tactile words like take, hold, purpose, result.
They're there for good reason. The experience of use is powerful, intimate, primal. For a long time, use was considered to be the defining trait that makes us human. We now know that not to be the case—check out this crow—but use is still absolutely central and fundamental to human experience.
"Customer" is a status someone receives by virtue of having conducted a transaction with you. "User" means something more—a direct engagement with your product or service in a concrete and meaningful way. If anything, "customer" is the abstraction here.
If, as you say, “the word 'user' abstracts the actual individual” in conversations in your organization, the problem isn't with the word. The problem is with how you're using it. If you elevate and honor the experience of use—and the thoughts, feelings, behaviors, and sensations that make up that experience—the notion of a “user” never turns into “a massive abstraction away from real problems people feel on a daily basis”. It gets you closer to the people you seek to serve, not farther away.
You say that you don't want to be thought of as a user. But you should. Because a user is the person to whom value must be delivered. A customer is simply the person from whom money must be acquired. Which one is more dehumanizing? Besides, we already had an era in which organizations focused on their customers—it was called the 20th Century. Look where that got us: a world full of products and services that collectively grind at us in order to shape our behavior to their requirements.
Now, a lot of people see this the same way you do, concluding that they should focus on “customers” and not “users”. And to be fair, they come to this conclusion with all the best intentions to get their organizations talking about people, so that they might treat those people in a more human (and humane) way. They say it's too late to save “user” from its roots in technology, and that any term with roots in technology must by definition be dehumanizing.
I don't buy that. There are many more organizations far beyond the technology industry that could benefit by shifting away from “customers” and toward “users” —and by doing so, reframe their products and services away from transactions and toward engagement through use. Elevate the user, and you change the way you think about the value you create in the world.
You say the word “customer” “immediately suggests a relationship we must deliver on”. And that's true. But do you really want to frame your business in terms of a set of transactional obligations? Aren't you going for something more?
Square is a disruptive business, there's no denying it. But think about the businesses you're disrupting. Don't you think their conversations revolve around “customers” and not “users”? Has that language really served them all that well? Moreover, the nature of Square's disruption in the marketplace is not simply that you're doing things differently—it's that you're doing things differently with the experience of your users in mind.
You see Jack, your focus on “users” over “customers” is not your weakness. It's your strength. Don't leave it behind.