After its rapid and quite global adoption the "hamburger icon" is starting to face some critique. One of the writings on the subject is "The Hamburger Menu Doesn't Work" by James Archer, subtitled "It's a beautiful, elegant solution that gets it all wrong, and it's time to move on": http://deep.design/the-hamburger-menu/
And it's in this article that we find the following passage, describing the common notion of this widget (not necessarily representing the views of the author):
"This design pattern accomplishes a major goal by preserving precious real estate on mobile, tablet, or other small screens, and it’s consistent with the logic of the progressive disclosure design pattern." (James Archer)
Right? Just a moment, — "and it’s consistent with the logic of the progressive disclosure design pattern."
And this is the crucial misconception. Progressive disclosure as defined and used by Xerox is about objects and related actions. And it's all about visible objects!
(Mind the classic example of a square in a drawing application: Clicking the shape discloses editing functions and displays handles to size the object.)
"A subtle thing happens when everything is visible: the display becomes reality. The user model becomes identical with what is on the screen. Objects can be understood purely in terms of their visible characteristics. Actions can be understood in terms of their effects on the screen. (…) In Star, we have tried to make the objects and actions in the system visible."
(Designing the Star User Interface; David Canfield Smith; Byte, Issue 4/1982)
And here is the real problem: The hamburger icon as used today has no other object but the global context. By exposing context to the global context, it's a mere apropos without an object the user might relate to.
When Norm Cox designed the original icon for the Xerox Star user interface, it was a visual anchor for a menu revealing contextual functions to the visible content of the document. (Like selecting rows, etc.1) This is notably something else than the global, quite abstract context of a site navigation, disclosing navigational functions to address off-screen content.
Today's hamburger icon is just a paradigmatic misunderstanding.
To put this more clearly:
The hamburger icon/menu (as used today) introduces a metaphor of its own that is not consistent with progressive disclosure as used elsewhere in common interfaces (see above). It's more a "and here is the rest that you may be missing"-icon that isn't motivated by any consistent notion of the interface, but by concern for screen real estate. As a user, we may not assume the content of the menu but by empirical knowledge and by considering functions that we are missing and that may be hidden somewhere. Being related to the visible content only by negativity, it essentially breaks the model of the display as an on-screen reality.
Rather than being yet another interface element, the modern hamburger menu is the application. Its content may be related to only by expectations and assumptions regarding the extent of the application's basic functionality. Arguably, in the light of this considerations, the icon is communicating rather sparsely what it is and what it does. (Actually, it exposes a global, unrelated view on the basic extent of the app.)
While its use may be arguable for an application (esp. mobile apps), it's highly problematic, when used in web sites and web applications.
(The difference: While in the former case it's located rather in the window chrome, thus relating to the viewport as an object, it's part of the view in the latter – like a wormhole to the global context.)
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Edit: Maybe things were clearer, if we were calling the Hamburger icon a (contextual) break-out button.
Are three stacked lines communicating a break-out? Hardly.