If you're laying out an interactive touch UI element, such as a button, you want something with a sensible physical size, so the user can hit it comfortably. In this way, laying out a touch UI is just like laying out physical buttons and knobs on an electronic device. And for this kind of physical engineering, millimeters (or inches) are the unit of choice.
For some reason this doesn't seem to be the case in touch UI design. I don't consider myself extremely well-read in the subject, but I've honestly never seen anybody use mm as a unit in, say, an Android layout file. But I've seen endless debates about "px" vs "dp" vs "sp" vs who knows what.
The "device-independent pixel" (which on Android is defined in terms of physical length - 1dp ≈ 0.16mm) seems like a really convoluted way to specify a length.
Why not just use millimeters?
Is it a problem with devices not supporting these units properly? Is it a cultural thing (programmers might be more used to thinking in "some sorta pixels" rather than physical units)? What's going on?
Generally, you'll find mobile usability folks talking about millimeters. But programmers and visual designers talk about density-independent pixels or points (1 Android "DIP" = 1 iOS "point") because even if you could specify a measurement in millimeters exactly, you'd end up with rounding issues or half-pixel anti-aliasing ugliness:
1mm equals 6.3 DIP (degree of precision there depends on the exact DPI value of the screen, since dip are quantized to the nearest of 120/160/240/320/480/640 dpi). That means on a standard G1-style 160DIP screen, if you specify a button as (let's say) 8mm, it'd be 50.4 pixels on that screen - good luck rendering that with any degree of precision, or telling Photoshop to end a line exactly 50.4px. And just rounding isn't much of a solution; the screen is still a fixed total width in pixels, and those rounding errors would compound in ways that mess up symmetry if you're (let's say) laying out a grid of buttons with specific sizes and padding amounts.
Specifying that as (let's say) 48DIP is much better, since that smoothly scales: 48px at 160DPI, 72px at HDPI (240) and 96px at 320DPI (AKA 2x in iOS terminology), no fractional pixel rendering or rounding needed.
As to why exactly the 160DPI pixel won out as the 1x mobile unit of measurement for the density-independent pixel, blame the first few iPhones and the HTC G1, which shared that configuration.