This was a bit of a UX WTF I uncovered when testing #1757504: Regression: language field is not visible on manage display.
When you're at a page like admin/structure/types/manage/article/display, the screen is split into "Visible" and "Hidden" fields, like so:

When you toggle the select box of Language from "Hidden" to "Visible" it will "pop" up into the other region of the page. However, if you use the drag handles to move it to, say, right below the Tags field, then upon saving you'll see it got snapped right back down to the "Hidden" region again. Sad panda.
Not sure that this is worth fixing really, since I'd much rather have a form builder-based Field UI that swentel was working on for awhile there. :) But figured I'd log it nonetheless.
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Comment #1
swentel commentedsee #1303412: 'Manage display' : Cannot drag in or out of 'Hidden'