The Document Profile preset (found on the Profile menu at the top of the New Document dialog), you choose can override your units setting in Preferences. If you choose a Profile that is geared for on-screen display—which is any of them except for "Print" and "Art & Illustration"—your units will default to pixels.
Side note: Generally, I disagree with anything overriding my settings in Preferences, but I understand why the unit-of-measure for on-screen profiles should be pixels. That said, by default the print-related profiles also will override your Preferences setting of milimeters and set your units to points. The good news is that when you change the units from the overriding default to your preferred milimeters in the New Document dialog, the Profile will change to "[Custom]," and it all it "sticks," so the next time you choose File > New, everything will be as it was that last time you clicked OK from the New Document dialog.